| |
| R version 3.6.2 Patched (2020-02-12 r77795) -- "Dark and Stormy Night" |
| Copyright (C) 2020 The R Foundation for Statistical Computing |
| Platform: x86_64-pc-linux-gnu (64-bit) |
| |
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| |
| > #### d|ensity |
| > #### p|robability (cumulative) |
| > #### q|uantile |
| > #### r|andom number generation |
| > #### |
| > #### Functions for ``d/p/q/r'' |
| > |
| > .ptime <- proc.time() |
| > F <- FALSE |
| > T <- TRUE |
| > |
| > options(warn = 2) |
| > ## ======== No warnings, unless explicitly asserted via |
| > assertWarning <- tools::assertWarning |
| > |
| > as.nan <- function(x) { x[is.na(x) & !is.nan(x)] <- NaN ; x } |
| > ###-- these are identical in ./arith-true.R ["fixme": use source(..)] |
| > opt.conformance <- 0 |
| > Meps <- .Machine $ double.eps |
| > xMax <- .Machine $ double.xmax |
| > options(rErr.eps = 1e-30) |
| > rErr <- function(approx, true, eps = getOption("rErr.eps", 1e-30)) |
| + { |
| + ifelse(Mod(true) >= eps, |
| + 1 - approx / true, # relative error |
| + true - approx) # absolute error (e.g. when true=0) |
| + } |
| > ## Numerical equality: Here want "rel.error" almost always: |
| > All.eq <- function(x,y) { |
| + all.equal.numeric(x,y, tolerance = 64*.Machine$double.eps, |
| + scale = max(0, mean(abs(x), na.rm=TRUE))) |
| + } |
| > if(!interactive()) |
| + set.seed(123) |
| > |
| > ## The prefixes of ALL the PDQ & R functions |
| > PDQRinteg <- c("binom", "geom", "hyper", "nbinom", "pois","signrank","wilcox") |
| > PDQR <- c(PDQRinteg, "beta", "cauchy", "chisq", "exp", "f", "gamma", |
| + "lnorm", "logis", "norm", "t","unif","weibull") |
| > PQonly <- c("tukey") |
| > |
| > ###--- Discrete Distributions --- Consistency Checks pZZ = cumsum(dZZ) |
| > |
| > ##for(pre in PDQRinteg) { n <- paste("d",pre,sep=""); cat(n,": "); str(get(n))} |
| > |
| > ##__ 1. Binomial __ |
| > |
| > ## Cumulative Binomial '==' Cumulative F : |
| > ## Abramowitz & Stegun, p.945-6; 26.5.24 AND 26.5.28 : |
| > n0 <- 50; n1 <- 16; n2 <- 20; n3 <- 8 |
| > for(n in rbinom(n1, size = 2*n0, p = .4)) { |
| + for(p in c(0,1,rbeta(n2, 2,4))) { |
| + for(k in rbinom(n3, size = n, prob = runif(1))) |
| + ## For X ~ Bin(n,p), compute 1 - P[X > k] = P[X <= k] in three ways: |
| + stopifnot(all.equal( pbinom(0:k, size = n, prob = p), |
| + cumsum(dbinom(0:k, size = n, prob = p))), |
| + all.equal(if(k==n || p==0) 1 else |
| + pf((k+1)/(n-k)*(1-p)/p, df1=2*(n-k), df2=2*(k+1)), |
| + sum(dbinom(0:k, size = n, prob = p)))) |
| + } |
| + } |
| > |
| > ##__ 2. Geometric __ |
| > for(pr in seq(1e-10,1,len=15)) # p=0 is not a distribution |
| + stopifnot(All.eq((dg <- dgeom(0:10, pr)), |
| + pr * (1-pr)^(0:10)), |
| + All.eq(cumsum(dg), pgeom(0:10, pr))) |
| > |
| > |
| > ##__ 3. Hypergeometric __ |
| > |
| > m <- 10; n <- 7 |
| > for(k in 2:m) { |
| + x <- 0:(k+1) |
| + stopifnot(All.eq(phyper(x, m, n, k), cumsum(dhyper(x, m, n, k)))) |
| + } |
| > |
| > ##__ 4. Negative Binomial __ |
| > |
| > ## PR #842 |
| > for(size in seq(0.8,2, by=.1)) |
| + stopifnot(all.equal(cumsum(dnbinom(0:7, size, .5)), |
| + pnbinom(0:7, size, .5))) |
| > stopifnot(All.eq(pnbinom(c(1,3), .9, .5), |
| + c(0.777035760338812, 0.946945347071519))) |
| > |
| > ##__ 5. Poisson __ |
| > |
| > stopifnot(dpois(0:5,0) == c(1, rep(0,5)), |
| + dpois(0:5,0, log=TRUE) == c(0, rep(-Inf, 5))) |
| > |
| > ## Cumulative Poisson '==' Cumulative Chi^2 : |
| > ## Abramowitz & Stegun, p.941 : 26.4.21 (26.4.2) |
| > n1 <- 20; n2 <- 16 |
| > for(lambda in rexp(n1)) |
| + for(k in rpois(n2, lambda)) |
| + stopifnot(all.equal(1 - pchisq(2*lambda, 2*(1+ 0:k)), |
| + pp <- cumsum(dpois(0:k, lambda=lambda)), |
| + tolerance = 100*Meps), |
| + all.equal(pp, ppois(0:k, lambda=lambda), tolerance = 100*Meps), |
| + all.equal(1 - pp, ppois(0:k, lambda=lambda, lower.tail = FALSE))) |
| > |
| > |
| > ##__ 6. SignRank __ |
| > for(n in rpois(32, lam=8)) { |
| + x <- -1:(n + 4) |
| + stopifnot(All.eq(psignrank(x, n), cumsum(dsignrank(x, n)))) |
| + } |
| > |
| > ##__ 7. Wilcoxon (symmetry & cumulative) __ |
| > is.sym <- TRUE |
| > for(n in rpois(5, lam=6)) |
| + for(m in rpois(15, lam=8)) { |
| + x <- -1:(n*m + 1) |
| + fx <- dwilcox(x, n, m) |
| + Fx <- pwilcox(x, n, m) |
| + is.sym <- is.sym & all(fx == dwilcox(x, m, n)) |
| + stopifnot(All.eq(Fx, cumsum(fx))) |
| + } |
| > stopifnot(is.sym) |
| > |
| > |
| > ###-------- Continuous Distributions ---------- |
| > |
| > ##--- Gamma (incl. central chi^2) Density : |
| > x <- round(rgamma(100, shape = 2),2) |
| > for(sh in round(rlnorm(30),2)) { |
| + Ga <- gamma(sh) |
| + for(sig in round(rlnorm(30),2)) |
| + stopifnot(all.equal((d1 <- dgamma( x, shape = sh, scale = sig)), |
| + (d2 <- dgamma(x/sig, shape = sh, scale = 1) / sig), |
| + tolerance = 1e-14)## __ad interim__ was 1e-15 |
| + , |
| + All.eq(d1, (d3 <- 1/(Ga * sig^sh) * x^(sh-1) * exp(-x/sig))) |
| + ) |
| + } |
| > |
| > stopifnot(pgamma(1,Inf,scale=Inf) == 0) |
| > ## Also pgamma(Inf,Inf) == 1 for which NaN was slightly more appropriate |
| > assertWarning(stopifnot( |
| + is.nan(c(pgamma(Inf, 1,scale=Inf), |
| + pgamma(Inf,Inf,scale=Inf))))) |
| > scLrg <- c(2,100, 1e300*c(.1, 1,10,100), 1e307, xMax, Inf) |
| > stopifnot(pgamma(Inf, 1, scale=xMax) == 1, |
| + pgamma(xMax,1, scale=Inf) == 0, |
| + all.equal(pgamma(1e300, 2, scale= scLrg, log=TRUE), |
| + c(0, 0, -0.000499523968713701, -1.33089326820406, |
| + -5.36470502873211, -9.91015144019122, |
| + -32.9293385491433, -38.707517174609, -Inf), |
| + tolerance = 2e-15) |
| + ) |
| > |
| > p <- 7e-4; df <- 0.9 |
| > stopifnot( |
| + abs(1-c(pchisq(qchisq(p, df),df)/p, # was 2.31e-8 for R <= 1.8.1 |
| + pchisq(qchisq(1-p, df,lower=FALSE),df,lower=FALSE)/(1-p),# was 1.618e-11 |
| + pchisq(qchisq(log(p), df,log=TRUE),df, log=TRUE)/log(p), # was 3.181e-9 |
| + pchisq(qchisq(log1p(-p),df,log=T,lower=F),df, log=T,lower=F)/log1p(-p) |
| + )# 32b-i386: (2.2e-16, 0,0, 3.3e-16); Opteron: (2.2e-16, 0,0, 2.2e-15) |
| + ) < 1e-14 |
| + ) |
| > |
| > ##-- non central Chi^2 : |
| > xB <- c(2000,1e6,1e50,Inf) |
| > for(df in c(0.1, 1, 10)) |
| + for(ncp in c(0, 1, 10, 100)) stopifnot(pchisq(xB, df=df, ncp=ncp) == 1) |
| > stopifnot(all.equal(qchisq(0.025,31,ncp=1,lower.tail=FALSE),# inf.loop PR#875 |
| + 49.7766246561514, tolerance = 1e-11)) |
| > for(df in c(0.1, 0.5, 1.5, 4.7, 10, 20,50,100)) { |
| + xx <- c(10^-(5:1), .9, 1.2, df + c(3,7,20,30,35,38)) |
| + pp <- pchisq(xx, df=df, ncp = 1) #print(pp) |
| + dtol <- 1e-12 *(if(2 < df && df <= 50) 64 else if(df > 50) 20000 else 501) |
| + stopifnot(all.equal(xx, qchisq(pp, df=df, ncp=1), tolerance = dtol)) |
| + } |
| > |
| > ## p ~= 1 (<==> 1-p ~= 0) -- gave infinite loop in R <= 1.8.1 -- PR#6421 |
| > psml <- 2^-(10:54) |
| > q0 <- qchisq(psml, df=1.2, ncp=10, lower.tail=FALSE) |
| > q1 <- qchisq(1-psml, df=1.2, ncp=10) # inaccurate in the tail |
| > p0 <- pchisq(q0, df=1.2, ncp=10, lower.tail=FALSE) |
| > p1 <- pchisq(q1, df=1.2, ncp=10, lower.tail=FALSE) |
| > iO <- 1:30 |
| > stopifnot(all.equal(q0[iO], q1[iO], tolerance = 1e-5),# 9.86e-8 |
| + all.equal(p0[iO], psml[iO])) # 1.07e-13 |
| > |
| > ##--- Beta (need more): |
| > |
| > ## big a & b (PR #643) |
| > stopifnot(is.finite(a <- rlnorm(20, 5.5)), a > 0, |
| + is.finite(b <- rlnorm(20, 6.5)), b > 0) |
| > pab <- expand.grid(seq(0,1,by=.1), a, b) |
| > p <- pab[,1]; a <- pab[,2]; b <- pab[,3] |
| > stopifnot(all.equal(dbeta(p,a,b), |
| + exp(pab <- dbeta(p,a,b, log = TRUE)), tolerance = 1e-11)) |
| > sp <- sample(pab, 50) |
| > if(!interactive()) |
| + stopifnot(which(isI <- sp == -Inf) == |
| + c(3, 10, 14, 18, 24, 32, 35, 41, 42, 45, 46, 47), |
| + all.equal(range(sp[!isI]), c(-2888.393250, 3.181137)) |
| + ) |
| > |
| > |
| > ##--- Normal (& Lognormal) : |
| > |
| > stopifnot( |
| + qnorm(0) == -Inf, qnorm(-Inf, log = TRUE) == -Inf, |
| + qnorm(1) == Inf, qnorm( 0, log = TRUE) == Inf) |
| > |
| > assertWarning(stopifnot( |
| + is.nan(qnorm(1.1)), |
| + is.nan(qnorm(-.1)))) |
| > |
| > x <- c(-Inf, -1e100, 1:6, 1e200, Inf) |
| > stopifnot( |
| + dnorm(x,3,s=0) == c(0,0,0,0, Inf, 0,0,0,0,0), |
| + pnorm(x,3,s=0) == c(0,0,0,0, 1 , 1,1,1,1,1), |
| + dnorm(x,3,s=Inf) == 0, |
| + pnorm(x,3,s=Inf) == c(0, rep(0.5, 8), 1)) |
| > |
| > ## 3 Test data from Wichura (1988) : |
| > stopifnot( |
| + all.equal(qnorm(c( 0.25, .001, 1e-20)), |
| + c(-0.6744897501960817, -3.090232306167814, -9.262340089798408), |
| + tolerance = 1e-15) |
| + , ## extreme tail -- available on log scale only: |
| + all.equal(qnorm(-1e5, log = TRUE), -447.1974945) |
| + ) |
| > |
| > z <- rnorm(1000); all.equal(pnorm(z), 1 - pnorm(-z), tolerance = 1e-15) |
| [1] TRUE |
| > z <- c(-Inf,Inf,NA,NaN, rt(1000, df=2)) |
| > z.ok <- z > -37.5 | !is.finite(z) |
| > for(df in 1:10) stopifnot(all.equal(pt(z, df), 1 - pt(-z,df), tolerance = 1e-15)) |
| > |
| > stopifnot(All.eq(pz <- pnorm(z), 1 - pnorm(z, lower=FALSE)), |
| + All.eq(pz, pnorm(-z, lower=FALSE)), |
| + All.eq(log(pz[z.ok]), pnorm(z[z.ok], log=TRUE))) |
| > y <- seq(-70,0, by = 10) |
| > cbind(y, "log(pnorm(y))"= log(pnorm(y)), "pnorm(y, log=T)"= pnorm(y, log=TRUE)) |
| y log(pnorm(y)) pnorm(y, log=T) |
| [1,] -70 -Inf -2455.1676378 |
| [2,] -60 -Inf -1805.0135607 |
| [3,] -50 -Inf -1254.8313611 |
| [4,] -40 -Inf -804.6084420 |
| [5,] -30 -454.3212440 -454.3212440 |
| [6,] -20 -203.9171554 -203.9171554 |
| [7,] -10 -53.2312852 -53.2312852 |
| [8,] 0 -0.6931472 -0.6931472 |
| > y <- c(1:15, seq(20,40, by=5)) |
| > cbind(y, "log(pnorm(y))"= log(pnorm(y)), "pnorm(y, log=T)"= pnorm(y, log=TRUE), |
| + "log(pnorm(-y))"= log(pnorm(-y)), "pnorm(-y, log=T)"= pnorm(-y, log=TRUE)) |
| y log(pnorm(y)) pnorm(y, log=T) log(pnorm(-y)) pnorm(-y, log=T) |
| [1,] 1 -1.727538e-01 -1.727538e-01 -1.841022 -1.841022 |
| [2,] 2 -2.301291e-02 -2.301291e-02 -3.783184 -3.783184 |
| [3,] 3 -1.350810e-03 -1.350810e-03 -6.607726 -6.607726 |
| [4,] 4 -3.167174e-05 -3.167174e-05 -10.360101 -10.360101 |
| [5,] 5 -2.866516e-07 -2.866516e-07 -15.064998 -15.064998 |
| [6,] 6 -9.865877e-10 -9.865876e-10 -20.736769 -20.736769 |
| [7,] 7 -1.279865e-12 -1.279813e-12 -27.384307 -27.384307 |
| [8,] 8 -6.661338e-16 -6.220961e-16 -35.013437 -35.013437 |
| [9,] 9 0.000000e+00 -1.128588e-19 -43.628149 -43.628149 |
| [10,] 10 0.000000e+00 -7.619853e-24 -53.231285 -53.231285 |
| [11,] 11 0.000000e+00 -1.910660e-28 -63.824934 -63.824934 |
| [12,] 12 0.000000e+00 -1.776482e-33 -75.410673 -75.410673 |
| [13,] 13 0.000000e+00 -6.117164e-39 -87.989720 -87.989720 |
| [14,] 14 0.000000e+00 -7.793537e-45 -101.563034 -101.563034 |
| [15,] 15 0.000000e+00 -3.670966e-51 -116.131385 -116.131385 |
| [16,] 20 0.000000e+00 -2.753624e-89 -203.917155 -203.917155 |
| [17,] 25 0.000000e+00 -3.056697e-138 -316.639408 -316.639408 |
| [18,] 30 0.000000e+00 -4.906714e-198 -454.321244 -454.321244 |
| [19,] 35 0.000000e+00 -1.124911e-268 -616.975101 -616.975101 |
| [20,] 40 0.000000e+00 0.000000e+00 -Inf -804.608442 |
| > ## Symmetry: |
| > y <- c(1:50,10^c(3:10,20,50,150,250)) |
| > y <- c(-y,0,y) |
| > for(L in c(FALSE,TRUE)) |
| + stopifnot(identical(pnorm(-y, log= L), |
| + pnorm(+y, log= L, lower=FALSE))) |
| > |
| > ## Log norm |
| > stopifnot(All.eq(pz, plnorm(exp(z)))) |
| > |
| > |
| > ###========== p <-> q Inversion consistency ===================== |
| > ok <- 1e-5 < pz & pz < 1 - 1e-5 |
| > all.equal(z[ok], qnorm(pz[ok]), tolerance = 1e-12) |
| [1] TRUE |
| > |
| > ###===== Random numbers -- first, just output: |
| > |
| > set.seed(123) |
| > # .Random.seed <- c(0L, 17292L, 29447L, 24113L) |
| > n <- 20 |
| > ## for(pre in PDQR) { n <- paste("r",pre,sep=""); cat(n,": "); str(get(n))} |
| > (Rbeta <- rbeta (n, shape1 = .8, shape2 = 2) ) |
| [1] 0.554206761 0.387924405 0.012541339 0.257889595 0.236064413 0.008248085 |
| [7] 0.136510774 0.618501837 0.028641308 0.151670292 0.242835922 0.551824427 |
| [13] 0.127798688 0.087335901 0.509096247 0.382121566 0.773494885 0.639404676 |
| [19] 0.066559813 0.227487378 |
| > (Rbinom <- rbinom (n, size = 55, prob = pi/16) ) |
| [1] 7 13 15 10 12 7 10 9 13 10 13 13 13 10 13 12 12 3 11 8 |
| > (Rcauchy <- rcauchy (n, location = 12, scale = 2) ) |
| [1] 17.042930 6.592944 15.980645 12.728113 13.921385 8.570544 19.557102 |
| [8] 10.430404 12.669798 21.641273 11.905411 11.301537 11.254793 13.226057 |
| [15] 12.870672 8.167569 15.735143 8.272588 15.159679 13.338095 |
| > (Rchisq <- rchisq (n, df = 3) ) |
| [1] 3.8641030 1.8367371 1.2291085 1.9151780 2.5901414 0.4522238 0.1018120 |
| [8] 0.4323865 2.4551985 2.8313420 1.1215175 8.6109152 0.2215425 2.6531221 |
| [15] 2.9968656 2.1074132 4.2698236 8.2015930 1.1384935 0.6041294 |
| > (Rexp <- rexp (n, rate = 2) ) |
| [1] 0.719726313 0.232135206 0.134439025 0.731650280 0.768696989 0.002299563 |
| [7] 0.554382734 0.149985159 0.596001504 0.557464352 0.033687945 0.240334360 |
| [13] 0.785227170 0.129973053 0.928461144 0.231609810 0.118017873 0.591049711 |
| [19] 0.029835686 0.201619221 |
| > (Rf <- rf (n, df1 = 12, df2 = 6) ) |
| [1] 0.7630651 0.4158576 0.4052799 0.8862771 2.0435073 2.5383554 0.8259689 |
| [8] 1.5831584 0.6362728 0.7221707 1.1665204 0.4821276 1.1985013 0.8955592 |
| [15] 1.5186453 0.7333794 0.3795005 0.7464008 1.5543317 5.8525268 |
| > (Rgamma <- rgamma (n, shape = 2, scale = 5) ) |
| [1] 11.843056 6.993596 12.413160 5.980309 5.970495 15.674812 7.382163 |
| [8] 11.343789 5.392676 3.766812 15.331767 2.451095 13.046780 10.999054 |
| [15] 9.929606 6.239055 3.588397 26.196937 3.647236 23.051571 |
| > (Rgeom <- rgeom (n, prob = pi/16) ) |
| [1] 8 2 4 2 3 5 5 4 1 8 1 6 1 6 8 3 8 7 5 0 |
| > (Rhyper <- rhyper (n, m = 40, n = 30, k = 20) ) |
| [1] 12 11 12 10 13 11 13 13 8 12 12 15 11 11 11 12 9 11 12 12 |
| > (Rlnorm <- rlnorm (n, meanlog = -1, sdlog = 3) ) |
| [1] 1.873201e-02 5.609747e+01 9.793124e-02 4.203730e-02 9.015415e-03 |
| [6] 7.795979e-03 6.574837e-02 2.348924e+00 1.027326e+01 3.073340e+00 |
| [11] 1.235670e-01 4.401014e-01 4.443226e-02 4.278129e-02 5.227596e+00 |
| [16] 1.747860e-02 1.297853e+02 2.805625e-01 7.002040e-01 4.013193e-02 |
| > (Rlogis <- rlogis (n, location = 12, scale = 2) ) |
| [1] 10.139287 14.905198 7.466552 15.060325 11.415297 14.260524 13.347886 |
| [8] 11.554385 13.039986 -3.344515 9.436395 13.741216 9.411881 14.951552 |
| [15] 10.378811 13.579174 17.257244 7.933965 8.157203 13.491243 |
| > (Rnbinom <- rnbinom (n, size = 7, prob = .01) ) |
| [1] 563 315 519 707 614 637 560 1086 1088 842 522 787 576 673 607 |
| [16] 443 1023 590 663 947 |
| > (Rnorm <- rnorm (n, mean = -1, sd = 3) ) |
| [1] -0.3732778 -5.6447208 -4.5214067 2.5364456 -2.2579283 -6.5577259 |
| [7] 0.4577794 -2.4157378 1.5402158 1.7773118 -1.9624917 -4.9029209 |
| [13] 6.3787040 1.3350950 1.0696427 -6.1133966 2.3161164 -1.9415584 |
| [19] -2.0400782 2.1153214 |
| > (Rpois <- rpois (n, lambda = 12) ) |
| [1] 10 15 14 9 15 12 16 7 7 14 11 14 16 12 15 7 7 13 15 12 |
| > (Rsignrank<- rsignrank(n, n = 47) ) |
| [1] 531 522 385 583 731 461 542 590 485 582 571 475 702 537 395 571 603 515 477 |
| [20] 609 |
| > (Rt <- rt (n, df = 11) ) |
| [1] -0.499846093 -1.670698483 -0.729757704 0.009882459 1.518830804 |
| [6] -1.105480914 -0.073913420 -0.323601935 -0.309210484 1.071490670 |
| [11] -1.730648357 -0.283141485 0.205309956 0.409676847 3.137494386 |
| [16] 0.187070891 -1.154130926 0.970408359 -1.340678412 1.437769232 |
| > ## Rt2 below (to preserve the following random numbers!) |
| > (Runif <- runif (n, min = .2, max = 2) ) |
| [1] 1.3077353 0.6915398 0.3146723 0.3301459 1.7723202 0.8530850 1.9021199 |
| [8] 1.2049741 1.1227901 1.9059890 0.3976429 1.6740336 0.8792158 1.2019539 |
| [15] 0.7649681 0.3482172 1.6038876 0.5478225 1.3800538 0.9832647 |
| > (Rweibull <- rweibull (n, shape = 3, scale = 2) ) |
| [1] 2.3507552 0.3498804 1.8610901 3.0250054 0.8043691 1.0338586 1.5966081 |
| [8] 2.1295946 1.1916615 0.7320637 1.0860054 2.5452588 0.6323843 1.6726976 |
| [15] 3.4711560 2.5185134 3.4519830 1.1740161 1.2526410 0.8298120 |
| > (Rwilcox <- rwilcox (n, m = 13, n = 17) ) |
| [1] 80 92 104 92 116 55 115 105 102 133 98 116 149 118 93 73 126 126 124 |
| [20] 99 |
| > (Rt2 <- rt (n, df = 1.01)) |
| [1] -0.4507473 7.9567158 1.9317506 -4.5681636 -0.7939303 -1.3143350 |
| [7] -0.2751314 -1.2305970 -1.2321505 2.2912240 4.3743122 -1.3400950 |
| [13] -0.4901184 0.7864050 0.9570928 50.6881882 0.2577983 0.2478237 |
| [19] 1.3330087 0.3807687 |
| > |
| > (Pbeta <- pbeta (Rbeta, shape1 = .8, shape2 = 2) ) |
| [1] 0.84605840 0.69836904 0.05389148 0.53895245 0.50764485 0.03861536 |
| [7] 0.34373485 0.88868811 0.10358645 0.37126511 0.51751532 0.84433212 |
| [13] 0.32741433 0.24605563 0.81153016 0.69214938 0.96181357 0.90094249 |
| [19] 0.19989455 0.49493375 |
| > (Pbinom <- pbinom (Rbinom, size = 55, prob = pi/16) ) |
| [1] 0.128811009 0.822082686 0.939887897 0.473358125 0.725714645 0.128811009 |
| [7] 0.473358125 0.340181320 0.822082686 0.473358125 0.822082686 0.822082686 |
| [13] 0.822082686 0.473358125 0.822082686 0.725714645 0.725714645 0.002917878 |
| [19] 0.606468256 0.221684127 |
| > (Pcauchy <- pcauchy (Rcauchy, location = 12, scale = 2) ) |
| [1] 0.8798165 0.1127710 0.8517979 0.6111354 0.7436195 0.1680556 0.9176468 |
| [8] 0.2881958 0.6028646 0.9348927 0.4849570 0.3930511 0.3864691 0.6750527 |
| [15] 0.6306957 0.1531019 0.8435165 0.1567581 0.8203732 0.6876911 |
| > (Pchisq <- pchisq (Rchisq, df = 3) ) |
| [1] 0.723482597 0.393026646 0.253968309 0.409802926 0.540779498 0.070744975 |
| [7] 0.008380908 0.066526148 0.516557851 0.581633585 0.228117628 0.965062738 |
| [13] 0.025961119 0.551747428 0.607891302 0.449585516 0.766236467 0.957975966 |
| [19] 0.232209338 0.104513603 |
| > (Pexp <- pexp (Rexp, rate = 2) ) |
| [1] 0.762942518 0.371406447 0.235763552 0.768528971 0.785059488 0.004588567 |
| [7] 0.670033937 0.259159790 0.696387483 0.672061341 0.065156264 0.381630263 |
| [13] 0.792049319 0.228906859 0.843847516 0.370745580 0.210247557 0.693365692 |
| [19] 0.057925925 0.331847235 |
| > (Pf <- pf (Rf, df1 = 12, df2 = 6) ) |
| [1] 0.32410218 0.09232470 0.08630331 0.40259602 0.80440198 0.86907389 |
| [7] 0.36505563 0.70322821 0.23758524 0.29664970 0.55170692 0.13291359 |
| [13] 0.56607937 0.40821091 0.68428769 0.30422992 0.07227779 0.31298492 |
| [19] 0.69494050 0.97980295 |
| > (Pgamma <- pgamma (Rgamma, shape = 2, scale = 5) ) |
| [1] 0.6846621 0.4077251 0.7091198 0.3359489 0.3352389 0.8201234 0.4342559 |
| [8] 0.6618778 0.2931040 0.1745504 0.8105456 0.0872524 0.7344167 0.6453838 |
| [15] 0.5901700 0.3545801 0.1619732 0.9669094 0.1661030 0.9441847 |
| > (Pgeom <- pgeom (Rgeom, prob = pi/16) ) |
| [1] 0.8601686 0.4809591 0.6647753 0.4809591 0.5828725 0.7305965 0.7305965 |
| [8] 0.6647753 0.3541459 0.8601686 0.3541459 0.7834938 0.3541459 0.7834938 |
| [15] 0.8601686 0.5828725 0.8601686 0.8260047 0.7305965 0.1963495 |
| > (Phyper <- phyper (Rhyper, m = 40, n = 30, k = 20) ) |
| [1] 0.71494883 0.51295659 0.71494883 0.30864260 0.86627413 0.51295659 |
| [7] 0.86627413 0.86627413 0.05904998 0.71494883 0.71494883 0.98680472 |
| [13] 0.51295659 0.51295659 0.51295659 0.71494883 0.15132082 0.51295659 |
| [19] 0.71494883 0.71494883 |
| > (Plnorm <- plnorm (Rlnorm, meanlog = -1, sdlog = 3) ) |
| [1] 0.16047510 0.95310121 0.32954742 0.23481968 0.10817853 0.09944582 |
| [7] 0.28299287 0.73170766 0.86646776 0.76039954 0.35805697 0.52382260 |
| [13] 0.24053070 0.23661975 0.81182742 0.15491172 0.97472581 0.46401663 |
| [19] 0.58493655 0.23009692 |
| > (Plogis <- plogis (Rlogis, location = 12, scale = 2) ) |
| [1] 0.2828523996 0.8103980662 0.0939166071 0.8220300712 0.4274282807 |
| [6] 0.7558872597 0.6623855066 0.4445273969 0.6271461844 0.0004653491 |
| [11] 0.2172435140 0.7048722457 0.2151664882 0.8139337213 0.3077638743 |
| [16] 0.6877426857 0.9326810790 0.1157796648 0.1277056879 0.6782238574 |
| > (Pnbinom <- pnbinom (Rnbinom, size = 7, prob = .01) ) |
| [1] 0.34539127 0.04498289 0.27616523 0.57177025 0.42755552 0.46435569 |
| [7] 0.34059007 0.91950991 0.92034921 0.74409223 0.28078034 0.68045166 |
| [13] 0.36627489 0.52069882 0.41628414 0.16798077 0.88887110 0.38885301 |
| [19] 0.50524696 0.83942274 |
| > (Pnorm <- pnorm (Rnorm, mean = -1, sd = 3) ) |
| [1] 0.58273974 0.06078223 0.12023713 0.88076412 0.33749500 0.03197163 |
| [7] 0.68649035 0.31849459 0.80142958 0.82271739 0.37416939 0.09663374 |
| [13] 0.99304478 0.78182307 0.75486546 0.04414707 0.86550081 0.37681641 |
| [19] 0.36441108 0.85046748 |
| > (Ppois <- ppois (Rpois, lambda = 12) ) |
| [1] 0.3472294 0.8444157 0.7720245 0.2423922 0.8444157 0.5759652 0.8987090 |
| [8] 0.0895045 0.0895045 0.7720245 0.4615973 0.7720245 0.8987090 0.5759652 |
| [15] 0.8444157 0.0895045 0.0895045 0.6815356 0.8444157 0.5759652 |
| > (Psignrank<- psignrank(Rsignrank, n = 47) ) |
| [1] 0.36663746 0.33169387 0.02921581 0.58098562 0.96191228 0.14044836 |
| [7] 0.41083885 0.60942723 0.20480997 0.57688473 0.53132960 0.17614726 |
| [13] 0.92806867 0.39057277 0.03720129 0.53132960 0.66065154 0.30545809 |
| [19] 0.18167093 0.68340768 |
| > (Pt <- pt (Rt, df = 11) ) |
| [1] 0.31351556 0.06147847 0.24039508 0.50385399 0.92149468 0.14627181 |
| [7] 0.47120313 0.37615421 0.38146974 0.84655256 0.05571530 0.39116296 |
| [13] 0.57946003 0.65504612 0.99527474 0.57249461 0.13645270 0.82365134 |
| [19] 0.10352754 0.91083331 |
| > (Pt2 <- pt (Rt2, df = 1.01) ) |
| [1] 0.36490878 0.96094812 0.84890254 0.06767383 0.28587141 0.20622746 |
| [7] 0.41436382 0.21644090 0.21624373 0.86999347 0.92939659 0.20324856 |
| [13] 0.35461982 0.71264902 0.74365588 0.99395091 0.58047323 0.57748238 |
| [19] 0.79593933 0.61605276 |
| > (Punif <- punif (Runif, min = .2, max = 2) ) |
| [1] 0.61540849 0.27307767 0.06370684 0.07230328 0.87351121 0.36282500 |
| [7] 0.94562215 0.55831894 0.51266115 0.94777166 0.10980160 0.81890755 |
| [13] 0.37734211 0.55664105 0.31387119 0.08234288 0.77993754 0.19323473 |
| [19] 0.65558547 0.43514705 |
| > (Pweibull <- pweibull (Rweibull, shape = 3, scale = 2) ) |
| [1] 0.802851673 0.005339578 0.553257134 0.968573336 0.062983442 0.129016046 |
| [7] 0.398753717 0.700984544 0.190653725 0.047857615 0.147946029 0.872690264 |
| [13] 0.031117650 0.442898991 0.994635553 0.864236080 0.994152898 0.183125938 |
| [19] 0.217836412 0.068933714 |
| > (Pwilcox <- pwilcox (Rwilcox, m = 13, n = 17) ) |
| [1] 0.106381913 0.228522998 0.402346437 0.228522998 0.597653563 0.009833454 |
| [7] 0.581622297 0.418377703 0.370781167 0.829464624 0.310291237 0.597653563 |
| [13] 0.948370460 0.629218833 0.241282199 0.061358235 0.745593076 0.745593076 |
| [19] 0.718298294 0.325029106 |
| > |
| > dbeta (Rbeta, shape1 = .8, shape2 = 2) |
| [1] 0.7223732 1.0651681 3.4136000 1.4013424 1.4682944 3.7281631 1.8517657 |
| [8] 0.6047651 2.8467121 1.7813410 1.4470712 0.7268595 1.8952825 2.1401041 |
| [15] 0.8090938 1.0785126 0.3433595 0.5678419 2.3110352 1.4958106 |
| > dbinom (Rbinom, size = 55, prob = pi/16) |
| [1] 0.063354298 0.096368041 0.047170694 0.133176805 0.119246389 0.063354298 |
| [7] 0.133176805 0.118497194 0.096368041 0.133176805 0.096368041 0.096368041 |
| [13] 0.096368041 0.133176805 0.096368041 0.119246389 0.119246389 0.002298608 |
| [19] 0.133110131 0.092873118 |
| > dcauchy (Rcauchy, location = 12, scale = 2) |
| [1] 0.021630824 0.019154376 0.032078738 0.140529537 0.082766881 0.040391664 |
| [7] 0.010417640 0.098492589 0.143104718 0.006566194 0.158799748 0.141854068 |
| [13] 0.139752618 0.115681430 0.133797911 0.034066567 0.035463730 0.035578069 |
| [19] 0.045526265 0.109942144 |
| > dchisq (Rchisq, df = 3) |
| [1] 0.11359392 0.21581974 0.23922560 0.21190393 0.17584488 0.21398711 |
| [7] 0.12097660 0.21132681 0.18315290 0.16296267 0.24114522 0.01579786 |
| [13] 0.16808590 0.17245292 0.15434146 0.20191378 0.09748429 0.01891934 |
| [19] 0.24090989 0.22923980 |
| > dexp (Rexp, rate = 2) |
| [1] 0.4741150 1.2571871 1.5284729 0.4629421 0.4298810 1.9908229 0.6599321 |
| [8] 1.4816804 0.6072250 0.6558773 1.8696875 1.2367395 0.4159014 1.5421863 |
| [15] 0.3123050 1.2585088 1.5795049 0.6132686 1.8841481 1.3363055 |
| > df (Rf, df1 = 12, df2 = 6) |
| [1] 0.664042111 0.576090730 0.562274916 0.607318497 0.167959027 0.100284610 |
| [7] 0.637144174 0.282709564 0.693573655 0.678003283 0.457493848 0.643454728 |
| [13] 0.441386316 0.602499118 0.304762080 0.674516557 0.524996364 0.670131912 |
| [19] 0.292349736 0.008558897 |
| > dgamma (Rgamma, shape = 2, scale = 5) |
| [1] 0.044345445 0.069072391 0.041471424 0.072333682 0.072356861 0.027275042 |
| [7] 0.067458566 0.046936330 0.073360525 0.070933729 0.028572738 0.060051063 |
| [13] 0.038400284 0.048758423 0.054515175 0.071657454 0.070028735 0.005557423 |
| [19] 0.070344309 0.009173320 |
| > dgeom (Rgeom, prob = pi/16) |
| [1] 0.03416390 0.12681315 0.08190279 0.12681315 0.10191344 0.06582121 |
| [7] 0.06582121 0.08190279 0.15779640 0.03416390 0.15779640 0.05289725 |
| [13] 0.15779640 0.05289725 0.03416390 0.10191344 0.03416390 0.04251090 |
| [19] 0.06582121 0.19634954 |
| > dhyper (Rhyper, m = 40, n = 30, k = 20) |
| [1] 0.20199224 0.20431399 0.20199224 0.15732178 0.15132529 0.20431399 |
| [7] 0.15132529 0.15132529 0.04108936 0.20199224 0.20199224 0.03541012 |
| [13] 0.20431399 0.20431399 0.20431399 0.20199224 0.09227084 0.20431399 |
| [19] 0.20199224 0.20199224 |
| > dlnorm (Rlnorm, meanlog = -1, sdlog = 3) |
| [1] 4.3380954158 0.0005822436 1.2319845653 2.4357017049 6.8694422907 |
| [6] 7.4733929149 1.7154009417 0.0467724227 0.0069920836 0.0336865537 |
| [11] 1.0073244481 0.3016205039 2.3349967070 2.4034440204 0.0172006936 |
| [16] 4.5426601250 0.0001514856 0.4720497698 0.1855964185 2.5226771709 |
| > dlogis (Rlogis, location = 12, scale = 2) |
| [1] 0.1014234598 0.0768265203 0.0425481390 0.0731483166 0.1223666728 |
| [6] 0.0922608552 0.1118154736 0.1234613952 0.1169169239 0.0002325663 |
| [11] 0.0850243848 0.1040136815 0.0844349353 0.0757228093 0.1065226360 |
| [16] 0.1073763420 0.0313935419 0.0511873670 0.0556984726 0.1091181283 |
| > dnbinom (Rnbinom, size = 7, prob = .01) |
| [1] 0.0016012889 0.0006114669 0.0015340423 0.0014659766 0.0016087509 |
| [6] 0.0015899813 0.0015985567 0.0004225217 0.0004186957 0.0010719579 |
| [11] 0.0015404998 0.0012444310 0.0016100854 0.0015372764 0.0016118864 |
| [16] 0.0012822374 0.0005567006 0.0016141573 0.0015545113 0.0007531913 |
| > dnorm (Rnorm, mean = -1, sd = 3) |
| [1] 0.130110398 0.040112199 0.066772988 0.066380399 0.121789513 0.023907371 |
| [7] 0.118172118 0.118967900 0.092918367 0.086632832 0.126309889 0.057050581 |
| [13] 0.006458952 0.098226734 0.104819164 0.031112294 0.072188495 0.126589892 |
| [19] 0.125224300 0.077557930 |
| > dpois (Rpois, lambda = 12) |
| [1] 0.10483726 0.07239112 0.09048890 0.08736438 0.07239112 0.11436792 |
| [7] 0.05429334 0.04368219 0.04368219 0.09048890 0.11436792 0.09048890 |
| [13] 0.05429334 0.11436792 0.07239112 0.04368219 0.04368219 0.10557038 |
| [19] 0.07239112 0.11436792 |
| > dsignrank(Rsignrank, n = 47) |
| [1] 0.0039429676 0.0038018425 0.0007151971 0.0041008982 0.0009032331 |
| [6] 0.0023508267 0.0040737886 0.0040318201 0.0029828933 0.0041090875 |
| [11] 0.0041704554 0.0027222983 0.0014781510 0.0040203094 0.0008698303 |
| [16] 0.0041704554 0.0038520708 0.0036731856 0.0027749926 0.0037486048 |
| > dt (Rt, df = 11) |
| [1] 0.340823726 0.100413165 0.293668976 0.389968983 0.124439520 0.207270198 |
| [7] 0.388829635 0.368437694 0.370255866 0.214961569 0.091948602 0.373362745 |
| [13] 0.381142118 0.356119169 0.008424401 0.382627645 0.196428441 0.238239645 |
| [19] 0.157280563 0.138777161 |
| > dunif (Runif, min = .2, max = 2) |
| [1] 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 |
| [8] 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 |
| [15] 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 0.5555556 |
| > dweibull (Rweibull, shape = 3, scale = 2) |
| [1] 0.40854433 0.04566100 0.58026142 0.10784049 0.22734704 0.34911114 |
| [7] 0.57475176 0.50853257 0.43099423 0.19135106 0.37684466 0.30928353 |
| [13] 0.14529960 0.58452097 0.02423843 0.32292685 0.02612818 0.42221582 |
| [19] 0.46023762 0.24042036 |
| > dwilcox (Rwilcox, m = 13, n = 17) |
| [1] 0.007553976 0.012383032 0.015873676 0.012383032 0.016031266 0.001126580 |
| [7] 0.016163798 0.016031266 0.015486075 0.010799421 0.014448507 0.016031266 |
| [13] 0.004704515 0.015691594 0.012759201 0.005024180 0.013477697 0.013477697 |
| [19] 0.014141025 0.014737869 |
| > |
| > ## Check q*(p*(.)) = identity |
| > All.eq(Rbeta, qbeta (Pbeta, shape1 = .8, shape2 = 2)) |
| [1] TRUE |
| > All.eq(Rbinom, qbinom (Pbinom, size = 55, prob = pi/16)) |
| [1] TRUE |
| > All.eq(Rcauchy, qcauchy (Pcauchy, location = 12, scale = 2)) |
| [1] TRUE |
| > All.eq(Rchisq, qchisq (Pchisq, df = 3)) |
| [1] TRUE |
| > All.eq(Rexp, qexp (Pexp, rate = 2)) |
| [1] TRUE |
| > All.eq(Rf, qf (Pf, df1 = 12, df2 = 6)) |
| [1] TRUE |
| > All.eq(Rgamma, qgamma (Pgamma, shape = 2, scale = 5)) |
| [1] TRUE |
| > All.eq(Rgeom, qgeom (Pgeom, prob = pi/16)) |
| [1] TRUE |
| > All.eq(Rhyper, qhyper (Phyper, m = 40, n = 30, k = 20)) |
| [1] TRUE |
| > All.eq(Rlnorm, qlnorm (Plnorm, meanlog = -1, sdlog = 3)) |
| [1] TRUE |
| > All.eq(Rlogis, qlogis (Plogis, location = 12, scale = 2)) |
| [1] TRUE |
| > All.eq(Rnbinom, qnbinom (Pnbinom, size = 7, prob = .01)) |
| [1] TRUE |
| > All.eq(Rnorm, qnorm (Pnorm, mean = -1, sd = 3)) |
| [1] TRUE |
| > All.eq(Rpois, qpois (Ppois, lambda = 12)) |
| [1] TRUE |
| > All.eq(Rsignrank, qsignrank(Psignrank, n = 47)) |
| [1] TRUE |
| > All.eq(Rt, qt (Pt, df = 11)) |
| [1] TRUE |
| > All.eq(Rt2, qt (Pt2, df = 1.01)) |
| [1] TRUE |
| > All.eq(Runif, qunif (Punif, min = .2, max = 2)) |
| [1] TRUE |
| > All.eq(Rweibull, qweibull (Pweibull, shape = 3, scale = 2)) |
| [1] TRUE |
| > All.eq(Rwilcox, qwilcox (Pwilcox, m = 13, n = 17)) |
| [1] TRUE |
| > |
| > ## Same with "upper tail": |
| > All.eq(Rbeta, qbeta (1- Pbeta, shape1 = .8, shape2 = 2, lower=F)) |
| [1] TRUE |
| > All.eq(Rbinom, qbinom (1- Pbinom, size = 55, prob = pi/16, lower=F)) |
| [1] TRUE |
| > All.eq(Rcauchy, qcauchy (1- Pcauchy, location = 12, scale = 2, lower=F)) |
| [1] TRUE |
| > All.eq(Rchisq, qchisq (1- Pchisq, df = 3, lower=F)) |
| [1] TRUE |
| > All.eq(Rexp, qexp (1- Pexp, rate = 2, lower=F)) |
| [1] TRUE |
| > All.eq(Rf, qf (1- Pf, df1 = 12, df2 = 6, lower=F)) |
| [1] TRUE |
| > All.eq(Rgamma, qgamma (1- Pgamma, shape = 2, scale = 5, lower=F)) |
| [1] TRUE |
| > All.eq(Rgeom, qgeom (1- Pgeom, prob = pi/16, lower=F)) |
| [1] TRUE |
| > All.eq(Rhyper, qhyper (1- Phyper, m = 40, n = 30, k = 20, lower=F)) |
| [1] TRUE |
| > All.eq(Rlnorm, qlnorm (1- Plnorm, meanlog = -1, sdlog = 3, lower=F)) |
| [1] TRUE |
| > All.eq(Rlogis, qlogis (1- Plogis, location = 12, scale = 2, lower=F)) |
| [1] TRUE |
| > All.eq(Rnbinom, qnbinom (1- Pnbinom, size = 7, prob = .01, lower=F)) |
| [1] TRUE |
| > All.eq(Rnorm, qnorm (1- Pnorm, mean = -1, sd = 3,lower=F)) |
| [1] TRUE |
| > All.eq(Rpois, qpois (1- Ppois, lambda = 12, lower=F)) |
| [1] TRUE |
| > All.eq(Rsignrank, qsignrank(1- Psignrank, n = 47, lower=F)) |
| [1] TRUE |
| > All.eq(Rt, qt (1- Pt, df = 11, lower=F)) |
| [1] TRUE |
| > All.eq(Rt2, qt (1- Pt2, df = 1.01, lower=F)) |
| [1] TRUE |
| > All.eq(Runif, qunif (1- Punif, min = .2, max = 2, lower=F)) |
| [1] TRUE |
| > All.eq(Rweibull, qweibull (1- Pweibull, shape = 3, scale = 2, lower=F)) |
| [1] TRUE |
| > All.eq(Rwilcox, qwilcox (1- Pwilcox, m = 13, n = 17, lower=F)) |
| [1] TRUE |
| > |
| > ## Check q*(p* ( log ), log) = identity |
| > All.eq(Rbeta, qbeta (log(Pbeta), shape1 = .8, shape2 = 2, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rbinom, qbinom (log(Pbinom), size = 55, prob = pi/16, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rcauchy, qcauchy (log(Pcauchy), location = 12, scale = 2, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rchisq, qchisq (log(Pchisq), df = 3, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rexp, qexp (log(Pexp), rate = 2, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rf, qf (log(Pf), df1= 12, df2= 6, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rgamma, qgamma (log(Pgamma), shape = 2, scale = 5, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rgeom, qgeom (log(Pgeom), prob = pi/16, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rhyper, qhyper (log(Phyper), m = 40, n = 30, k = 20, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rlnorm, qlnorm (log(Plnorm), meanlog = -1, sdlog = 3, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rlogis, qlogis (log(Plogis), location = 12, scale = 2, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rnbinom, qnbinom (log(Pnbinom), size = 7, prob = .01, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rnorm, qnorm (log(Pnorm), mean = -1, sd = 3, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rpois, qpois (log(Ppois), lambda = 12, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rsignrank, qsignrank(log(Psignrank), n = 47, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rt, qt (log(Pt), df = 11, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rt2, qt (log(Pt2), df = 1.01, log=TRUE)) |
| [1] TRUE |
| > All.eq(Runif, qunif (log(Punif), min = .2, max = 2, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rweibull, qweibull (log(Pweibull), shape = 3, scale = 2, log=TRUE)) |
| [1] TRUE |
| > All.eq(Rwilcox, qwilcox (log(Pwilcox), m = 13, n = 17, log=TRUE)) |
| [1] TRUE |
| > |
| > ## same q*(p* (log) log) with upper tail: |
| > |
| > All.eq(Rbeta, qbeta (log1p(-Pbeta), shape1 = .8, shape2 = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rbinom, qbinom (log1p(-Pbinom), size = 55, prob = pi/16, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rcauchy, qcauchy (log1p(-Pcauchy), location = 12, scale = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rchisq, qchisq (log1p(-Pchisq), df = 3, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rexp, qexp (log1p(-Pexp), rate = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rf, qf (log1p(-Pf), df1 = 12, df2 = 6, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rgamma, qgamma (log1p(-Pgamma), shape = 2, scale = 5, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rgeom, qgeom (log1p(-Pgeom), prob = pi/16, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rhyper, qhyper (log1p(-Phyper), m = 40, n = 30, k = 20, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rlnorm, qlnorm (log1p(-Plnorm), meanlog = -1, sdlog = 3, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rlogis, qlogis (log1p(-Plogis), location = 12, scale = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rnbinom, qnbinom (log1p(-Pnbinom), size = 7, prob = .01, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rnorm, qnorm (log1p(-Pnorm), mean = -1, sd = 3, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rpois, qpois (log1p(-Ppois), lambda = 12, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rsignrank, qsignrank(log1p(-Psignrank), n = 47, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rt, qt (log1p(-Pt ), df = 11, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rt2, qt (log1p(-Pt2), df = 1.01, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Runif, qunif (log1p(-Punif), min = .2, max = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rweibull, qweibull (log1p(-Pweibull), shape = 3, scale = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(Rwilcox, qwilcox (log1p(-Pwilcox), m = 13, n = 17, lower=F, log=T)) |
| [1] TRUE |
| > |
| > |
| > ## Check log( upper.tail ): |
| > All.eq(log1p(-Pbeta), pbeta (Rbeta, shape1 = .8, shape2 = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pbinom), pbinom (Rbinom, size = 55, prob = pi/16, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pcauchy), pcauchy (Rcauchy, location = 12, scale = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pchisq), pchisq (Rchisq, df = 3, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pexp), pexp (Rexp, rate = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pf), pf (Rf, df1 = 12, df2 = 6, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pgamma), pgamma (Rgamma, shape = 2, scale = 5, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pgeom), pgeom (Rgeom, prob = pi/16, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Phyper), phyper (Rhyper, m = 40, n = 30, k = 20, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Plnorm), plnorm (Rlnorm, meanlog = -1, sdlog = 3, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Plogis), plogis (Rlogis, location = 12, scale = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pnbinom), pnbinom (Rnbinom, size = 7, prob = .01, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pnorm), pnorm (Rnorm, mean = -1, sd = 3, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Ppois), ppois (Rpois, lambda = 12, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Psignrank), psignrank(Rsignrank, n = 47, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pt), pt (Rt, df = 11, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pt2), pt (Rt2,df = 1.01, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Punif), punif (Runif, min = .2, max = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pweibull), pweibull (Rweibull, shape = 3, scale = 2, lower=F, log=T)) |
| [1] TRUE |
| > All.eq(log1p(-Pwilcox), pwilcox (Rwilcox, m = 13, n = 17, lower=F, log=T)) |
| [1] TRUE |
| > |
| > |
| > ### (Extreme) tail tests added more recently: |
| > All.eq(1, -1e-17/ pexp(qexp(-1e-17, log=TRUE),log=TRUE)) |
| [1] TRUE |
| > abs(pgamma(30,100, lower=FALSE, log=TRUE) + 7.3384686328784e-24) < 1e-36 |
| [1] TRUE |
| > All.eq(1, pcauchy(-1e20) / 3.18309886183791e-21) |
| [1] TRUE |
| > All.eq(1, pcauchy(+1e15, log=TRUE) / -3.18309886183791e-16)## PR#6756 |
| [1] TRUE |
| > x <- 10^(ex <- c(1,2,5*(1:5),50,100,200,300,Inf)) |
| > for(a in x[ex > 10]) ## improve pt() : cbind(x,t= pt(-x, df=1), C=pcauchy(-x)) |
| + stopifnot(all.equal(pt(-a, df=1), pcauchy(-a), tolerance = 1e-15)) |
| > ## for PR#7902: |
| > ex <- -c(rev(1/x), ex) |
| > All.eq(-x, qcauchy(pcauchy(-x))) |
| [1] TRUE |
| > All.eq(+x, qcauchy(pcauchy(+x, log=TRUE), log=TRUE)) |
| [1] TRUE |
| > All.eq(1/x, pcauchy(qcauchy(1/x))) |
| [1] TRUE |
| > All.eq(ex, pcauchy(qcauchy(ex, log=TRUE), log=TRUE)) |
| [1] TRUE |
| > II <- c(-Inf,Inf) |
| > stopifnot(pcauchy(II) == 0:1, qcauchy(0:1) == II, |
| + pcauchy(II, log=TRUE) == c(-Inf,0), |
| + qcauchy(c(-Inf,0), log=TRUE) == II) |
| > ## PR#15521 : |
| > p <- 1 - 1/4096 |
| > stopifnot(all.equal(qcauchy(p), 1303.7970381453319163, tolerance = 1e-14)) |
| > |
| > pr <- 1e-23 ## PR#6757 |
| > stopifnot(all.equal(pr^ 12, pbinom(11, 12, prob= pr,lower=FALSE), |
| + tolerance = 1e-12, scale= 1e-270)) |
| > ## pbinom(.) gave 0 in R 1.9.0 |
| > pp <- 1e-17 ## PR#6792 |
| > stopifnot(all.equal(2*pp, pgeom(1, pp), scale= 1e-20)) |
| > ## pgeom(.) gave 0 in R 1.9.0 |
| > |
| > x <- 10^(100:295) |
| > sapply(c(1e-250, 1e-25, 0.9, 1.1, 101, 1e10, 1e100), |
| + function(shape) |
| + All.eq(-x, pgamma(x, shape=shape, lower=FALSE, log=TRUE))) |
| [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE |
| > x <- 2^(-1022:-900) |
| > ## where all completely off in R 2.0.1 |
| > all.equal(pgamma(x, 10, log = TRUE) - 10*log(x), |
| + rep(-15.104412573076, length(x)), tolerance = 1e-12)# 3.984e-14 (i386) |
| [1] TRUE |
| > all.equal(pgamma(x, 0.1, log = TRUE) - 0.1*log(x), |
| + rep(0.0498724412598364, length(x)), tolerance = 1e-13)# 7e-16 (i386) |
| [1] TRUE |
| > |
| > All.eq(dpois( 10*1:2, 3e-308, log=TRUE), |
| + c(-7096.08037610806, -14204.2875435307)) |
| [1] TRUE |
| > All.eq(dpois(1e20, 1e-290, log=TRUE), -7.12801378828154e+22) |
| [1] TRUE |
| > ## all gave -Inf in R 2.0.1 |
| > |
| > |
| > ## Inf df in pf etc. |
| > # apparently pf(df2=Inf) worked in 2.0.1 (undocumented) but df did not. |
| > x <- c(1/pi, 1, pi) |
| > oo <- options(digits = 8) |
| > df(x, 3, 1e6) |
| [1] 0.72553184 0.46254030 0.03300701 |
| > df(x, 3, Inf) |
| [1] 0.725532165 0.462540989 0.033006719 |
| > pf(x, 3, 1e6) |
| [1] 0.18784423 0.60837436 0.97585435 |
| > pf(x, 3, Inf) |
| [1] 0.18784423 0.60837482 0.97585479 |
| > |
| > df(x, 1e6, 5) |
| [1] 0.158602071 0.610206081 0.061036395 |
| > df(x, Inf, 5) |
| [1] 0.15859792 0.61020761 0.06103637 |
| > pf(x, 1e6, 5) |
| [1] 0.0077295711 0.4158807972 0.9022692409 |
| > pf(x, Inf, 5) |
| [1] 0.0077292503 0.4158801870 0.9022693759 |
| > |
| > df(x, Inf, Inf)# (0, Inf, 0) - since 2.1.1 |
| [1] 0 Inf 0 |
| > pf(x, Inf, Inf)# (0, 1/2, 1) |
| [1] 0.0 0.5 1.0 |
| > |
| > pf(x, 5, Inf, ncp=0) |
| [1] 0.097730624 0.584119813 0.992270750 |
| > all.equal(pf(x, 5, 1e6, ncp=1), tolerance = 1e-6, |
| + c(0.065933194, 0.470879987, 0.978875867)) |
| [1] TRUE |
| > all.equal(pf(x, 5, 1e7, ncp=1), tolerance = 1e-6, |
| + c(0.06593309, 0.47088028, 0.97887641)) |
| [1] TRUE |
| > all.equal(pf(x, 5, 1e8, ncp=1), tolerance = 1e-6, |
| + c(0.0659330751, 0.4708802996, 0.9788764591)) |
| [1] TRUE |
| > pf(x, 5, Inf, ncp=1) |
| [1] 0.065933078 0.470880318 0.978876467 |
| > |
| > dt(1, Inf) |
| [1] 0.24197072 |
| > dt(1, Inf, ncp=0) |
| [1] 0.24197072 |
| > dt(1, Inf, ncp=1) |
| [1] 0.39894228 |
| > dt(1, 1e6, ncp=1) |
| [1] 0.39894208 |
| > dt(1, 1e7, ncp=1) |
| [1] 0.39894226 |
| > dt(1, 1e8, ncp=1) |
| [1] 0.39894227 |
| > dt(1, 1e10, ncp=1) # = Inf |
| [1] 0.39894228 |
| > ## Inf valid as from 2.1.1: df(x, 1e16, 5) was way off in 2.0.1. |
| > |
| > sml.x <- c(10^-c(2:8,100), 0) |
| > cbind(x = sml.x, `dt(x,*)` = dt(sml.x, df = 2, ncp=1)) |
| x dt(x,*) |
| [1,] 1e-02 0.21686052 |
| [2,] 1e-03 0.21468294 |
| [3,] 1e-04 0.21446517 |
| [4,] 1e-05 0.21444339 |
| [5,] 1e-06 0.21444121 |
| [6,] 1e-07 0.21444100 |
| [7,] 1e-08 0.21444097 |
| [8,] 1e-100 0.21444097 |
| [9,] 0e+00 0.21444097 |
| > ## small 'x' used to suffer from cancellation |
| > options(oo) |
| > x <- c(outer(1:12, 10^c(-3:2, 6:9, 10*(2:30)))) |
| > for(nu in c(.75, 1.2, 4.5, 999, 1e50)) { |
| + lfx <- dt(x, df=nu, log=TRUE) |
| + stopifnot(is.finite(lfx), All.eq(exp(lfx), dt(x, df=nu))) |
| + }## dt(1e160, 1.2, log=TRUE) was -Inf up to R 2.15.2 |
| > |
| > ## pf() with large df1 or df2 |
| > ## (was said to be PR#7099, but that is about non-central pchisq) |
| > nu <- 2^seq(25, 34, 0.5) |
| > target <- pchisq(1, 1) # 0.682... |
| > y <- pf(1, 1, nu) |
| > stopifnot(All.eq(pf(1, 1, Inf), target), |
| + diff(c(y, target)) > 0, # i.e. pf(1, 1, *) is monotone increasing |
| + abs(y[1] - (target - 7.21129e-9)) < 1e-11) # computed value |
| > ## non-monotone in R <= 2.1.0 |
| > |
| > stopifnot(pgamma(Inf, 1.1) == 1) |
| > ## didn't not terminate in R 2.1.x (only) |
| > |
| > ## qgamma(q, *) should give {0,Inf} for q={0,1} |
| > sh <- c(1.1, 0.5, 0.2, 0.15, 1e-2, 1e-10) |
| > stopifnot(Inf == qgamma(1, sh)) |
| > stopifnot(0 == qgamma(0, sh)) |
| > ## the first gave Inf, NaN, and 99.425 in R 2.1.1 and earlier |
| > |
| > ## In extreme left tail {PR#11030} |
| > p <- 10:123*1e-12 |
| > qg <- qgamma(p, shape=19) |
| > qg2<- qgamma(1:100 * 1e-9, shape=11) |
| > stopifnot(diff(qg, diff=2) < -6e-6, |
| + diff(qg2,diff=2) < -6e-6, |
| + abs(1 - pgamma(qg, 19)/ p) < 1e-13, |
| + All.eq(qg [1], 2.35047385139143), |
| + All.eq(qg2[30], 1.11512318734547)) |
| > ## was non-continuous in R 2.6.2 and earlier |
| > |
| > f2 <- c(0.5, 1:4) |
| > stopifnot(df(0, 1, f2) == Inf, |
| + df(0, 2, f2) == 1, |
| + df(0, 3, f2) == 0) |
| > ## only the last one was ok in R 2.2.1 and earlier |
| > |
| > x0 <- -2 * 10^-c(22,10,7,5) # ==> d*() warns about non-integer: |
| > assertWarning(fx0 <- dbinom(x0, size = 3, prob = 0.1)) |
| > stopifnot(fx0 == 0, pbinom(x0, size = 3, prob = 0.1) == 0) |
| > |
| > ## very small negatives were rounded to 0 in R 2.2.1 and earlier |
| > |
| > ## dbeta(*, ncp): |
| > db.x <- c(0, 5, 80, 405, 1280, 3125, 6480, 12005, 20480, 32805, |
| + 50000, 73205, 103680, 142805, 192080, 253125, 327680) |
| > a <- rlnorm(100) |
| > stopifnot(All.eq(a, dbeta(0, 1, a, ncp=0)), |
| + dbeta(0, 0.9, 2.2, ncp = c(0, a)) == Inf, |
| + All.eq(65536 * dbeta(0:16/16, 5,1), db.x), |
| + All.eq(exp(16 * log(2) + dbeta(0:16/16, 5,1, log=TRUE)), db.x) |
| + ) |
| > ## the first gave 0, the 2nd NaN in R <= 2.3.0; others use 'TRUE' values |
| > stopifnot(all.equal(dbeta(0.8, 0.5, 5, ncp=1000),# was way too small in R <= 2.6.2 |
| + 3.001852308909e-35), |
| + all.equal(1, integrate(dbeta, 0,1, 0.8, 0.5, ncp=1000)$value, |
| + tolerance = 1e-4), |
| + all.equal(1, integrate(dbeta, 0,1, 0.5, 200, ncp=720)$value), |
| + all.equal(1, integrate(dbeta, 0,1, 125, 200, ncp=2000)$value) |
| + ) |
| > |
| > ## df(*, ncp): |
| > x <- seq(0, 10, length=101) |
| > h <- 1e-7 |
| > dx.h <- (pf(x+h, 7, 5, ncp= 2.5) - pf(x-h, 7, 5, ncp= 2.5)) / (2*h) |
| > stopifnot(all.equal(dx.h, df(x, 7, 5, ncp= 2.5), tolerance = 1e-6),# (1.50 | 1.65)e-8 |
| + All.eq(df(0, 2, 4, ncp=x), df(1e-300, 2, 4, ncp=x)) |
| + ) |
| > |
| > ## qt(p ~ 0, df=1) - PR#9804 |
| > p <- 10^(-10:-20) |
| > qtp <- qt(p, df = 1) |
| > ## relative error < 10^-14 : |
| > stopifnot(abs(1 - p / pt(qtp, df=1)) < 1e-14) |
| > |
| > ## Similarly for df = 2 --- both for p ~ 0 *and* p ~ 1/2 |
| > ## P ~ 0 |
| > stopifnot(all.equal(qt(-740, df=2, log=TRUE), -exp(370)/sqrt(2))) |
| > ## P ~ 1 (=> p ~ 0.5): |
| > p.5 <- 0.5 + 2^(-5*(5:8)) |
| > stopifnot(all.equal(qt(p.5, df = 2), |
| + c(8.429369702179e-08, 2.634178031931e-09, |
| + 8.231806349784e-11, 2.572439484308e-12))) |
| > ## qt(<large>, log = TRUE) is now more finite and monotone (again!): |
| > stopifnot(all.equal(qt(-1000, df = 4, log=TRUE), |
| + -4.930611e108, tolerance = 1e-6)) |
| > qtp <- qt(-(20:850), df=1.2, log=TRUE, lower=FALSE) |
| > ##almost: stopifnot(all(abs(5/6 - diff(log(qtp))) < 1e-11)) |
| > stopifnot(abs(5/6 - quantile(diff(log(qtp)), pr=c(0,0.995))) < 1e-11) |
| > |
| > ## close to df=1 (where Taylor steps are important!): |
| > stopifnot(all.equal(-20, pt(qt(-20, df=1.02, log=TRUE), |
| + df=1.02, log=TRUE), tolerance = 1e-12), |
| + diff(lq <- log(qt(-2^-(10:600), df=1.1, log=TRUE))) > 0.6) |
| > lq1 <- log(qt(-2^-(20:600), df=1, log=TRUE)) |
| > lq2 <- log(qt(-2^-(20:600), df=2, log=TRUE)) |
| > stopifnot(mean(abs(diff(lq1) - log(2) )) < 1e-8, |
| + mean(abs(diff(lq2) - log(sqrt(2)))) < 4e-8) |
| > ## Case, where log.p=TRUE was fine, but log.p=FALSE (default) gave NaN: |
| > lp <- 40:406 |
| > stopifnot(all.equal(lp, -pt(qt(exp(-lp), 1.2), 1.2, log=TRUE), tolerance = 4e-16)) |
| > |
| > |
| > ## pbeta(*, log=TRUE) {toms708} -- now improved tail behavior |
| > x <- c(.01, .10, .25, .40, .55, .71, .98) |
| > pbval <- c(-0.04605755624088, -0.3182809860569, -0.7503593555585, |
| + -1.241555830932, -1.851527837938, -2.76044482378, -8.149862739881) |
| > stopifnot(all.equal(pbeta(x, 0.8, 2, lower=FALSE, log=TRUE), pbval), |
| + all.equal(pbeta(1-x, 2, 0.8, log=TRUE), pbval)) |
| > qq <- 2^(0:1022) |
| > df.set <- c(0.1, 0.2, 0.5, 1, 1.2, 2.2, 5, 10, 20, 50, 100, 500) |
| > for(nu in df.set) { |
| + pqq <- pt(-qq, df = nu, log=TRUE) |
| + stopifnot(is.finite(pqq)) |
| + } |
| > ## PR#14230 -- more extreme beta cases {should no longer rely on denormalized} |
| > x <- (256:512)/1024 |
| > P <- pbeta(x, 3, 2200, lower.tail=FALSE, log.p=TRUE) |
| > stopifnot(is.finite(P), P < -600, |
| + -.001 < (D3P <- diff(P, diff = 3)), D3P < 0, diff(D3P) < 0) |
| > ## all but the first 43 where -Inf in R <= 2.9.1 |
| > stopifnot(All.eq(pt(2^-30, df=10), |
| + 0.50000000036238542)) |
| > ## = .5+ integrate(dt, 0,2^-30, df=10, rel.tol=1e-20) |
| > |
| > ## rbinom(*, size) gave NaN for large size up to R <= 2.6.1 |
| > M <- .Machine$integer.max |
| > set.seed(7) |
| > tt <- table(rbinom(100, M, pr = 1e-9)) # had values in {0,2} only |
| > t2 <- table(rbinom(100, 10*M, pr = 1e-10)) |
| > stopifnot(names(tt) == 0:6, sum(tt) == 100, sum(t2) == 100) ## no NaN there |
| > |
| > ## qf() with large df1, df2 and/or small p: |
| > x <- 0.01; f1 <- 1e60; f2 <- 1e90 |
| > stopifnot(qf(1/4, Inf, Inf) == 1, |
| + all.equal(1, 1e-18/ pf(qf(1e-18, 12,50), 12,50), tolerance = 1e-10), |
| + abs(x - qf(pf(x, f1,f2, log.p=TRUE), f1,f2, log.p=TRUE)) < 1e-4) |
| > |
| > ## qbeta(*, log.p) for "border" case: |
| > stopifnot(is.finite(q0 <- qbeta(-1e10, 50,40, log.p=TRUE)), |
| + 1 == qbeta(-1e10, 2, 3, log.p=TRUE, lower=FALSE)) |
| > ## infinite loop or NaN in R <= 2.7.0 |
| > |
| > ## phyper(x, 0,0,0), notably for huge x |
| > stopifnot(all(phyper(c(0:3, 1e67), 0,0,0) == 1)) |
| > ## practically infinite loop and NaN in R <= 2.7.1 (PR#11813) |
| > |
| > ## plnorm(<= 0, . , log.p=TRUE) |
| > stopifnot(plnorm(-1:0, lower.tail=FALSE, log.p=TRUE) == 0, |
| + plnorm(-1:0, lower.tail=TRUE, log.p=TRUE) == -Inf) |
| > ## was wrongly == 'log.p=FALSE' up to R <= 2.7.1 (PR#11867) |
| > |
| > |
| > ## pchisq(df=0) was wrong in 2.7.1; then, upto 2.10.1, P*(0,0) gave 1 |
| > stopifnot(pchisq(c(-1,0,1), df=0) == c(0,0,1), |
| + pchisq(c(-1,0,1), df=0, lower.tail=FALSE) == c(1,1,0), |
| + ## for ncp >= 80, gave values >= 1 in 2.10.0 |
| + pchisq(500:700, 1.01, ncp = 80) <= 1) |
| > |
| > ## dnbinom for extreme size and/or mu : |
| > mu <- 20 |
| > d <- dnbinom(17, mu=mu, size = 1e11*2^(1:10)) - dpois(17, lambda=mu) |
| > stopifnot(d < 0, diff(d) > 0, d[1] < 1e-10) |
| > ## was wrong up to 2.7.1 |
| > ## The fix to the above, for x = 0, had a new cancellation problem |
| > mu <- 1e12 * 2^(0:20) |
| > stopifnot(all.equal(1/(1+mu), dnbinom(0, size = 1, mu = mu), tolerance = 1e-13)) |
| > ## was wrong in 2.7.2 (only) |
| > mu <- sort(outer(1:7, 10^c(0:10,50*(1:6)))) |
| > NB <- dnbinom(5, size=1e305, mu=mu, log=TRUE) |
| > P <- dpois (5, mu, log=TRUE) |
| > stopifnot(abs(rErr(NB,P)) < 9*Meps)# seen 2.5* |
| > ## wrong in 3.1.0 and earlier |
| > |
| > |
| > ## Non-central F for large x |
| > x <- 1e16 * 1.1 ^ (0:20) |
| > dP <- diff(pf(x, df1=1, df2=1, ncp=20, lower.tail=FALSE, log=TRUE)) |
| > stopifnot(-0.047 < dP, dP < -0.0455) |
| > ## pf(*, log) jumped to -Inf prematurely in 2.8.0 and earlier |
| > |
| > |
| > ## Non-central Chi^2 density for large x |
| > stopifnot(0 == dchisq(c(Inf, 1e80, 1e50, 1e40), df=10, ncp=1)) |
| > ## did hang in 2.8.0 and earlier (PR#13309). |
| > |
| > |
| > ## qbinom() .. particularly for large sizes, small prob: |
| > p.s <- c(.01, .001, .1, .25) |
| > pr <- (2:20)*1e-7 |
| > sizes <- 1000*(5000 + c(0,6,16)) + 279 |
| > k.s <- 0:15; q.xct <- rep(k.s, each=length(pr)) |
| > for(sz in sizes) { |
| + for(p in p.s) { |
| + qb <- qbinom(p=p, size = sz, prob=pr) |
| + pb <- qpois (p=p, lambda = sz * pr) |
| + stopifnot(All.eq(qb, pb)) |
| + } |
| + pp.x <- outer(pr, k.s, function(pr, q) pbinom(q, size = sz, prob=pr)) |
| + qq.x <- apply(pp.x, 2, function(p) qbinom(p, size = sz, prob=pr)) |
| + stopifnot(qq.x == q.xct) |
| + } |
| > ## do_search() in qbinom() contained a thinko up to 2.9.0 (PR#13711) |
| > |
| > |
| > ## pbeta(x, a,b, log=TRUE) for small x and a is ~ log-linear |
| > x <- 2^-(200:10) |
| > for(a in c(1e-8, 1e-12, 16e-16, 4e-16)) |
| + for(b in c(0.6, 1, 2, 10)) { |
| + dp <- diff(pbeta(x, a, b, log=TRUE)) # constant approximately |
| + stopifnot(sd(dp) / mean(dp) < 0.0007) |
| + } |
| > ## had accidental cancellation '1 - w' |
| > |
| > ## qgamma(p, a) for small a and (hence) small p |
| > ## pgamma(x, a) for very very small a |
| > a <- 2^-seq(10,1000, .25) |
| > q.1c <- qgamma(1e-100,a,lower.tail=FALSE) |
| > q.3c <- qgamma(1e-300,a,lower.tail=FALSE) |
| > p.1c <- pgamma(q.1c[q.1c > 0], a[q.1c > 0], lower.tail=FALSE) |
| > p.3c <- pgamma(q.3c[q.3c > 0], a[q.3c > 0], lower.tail=FALSE) |
| > x <- 1+1e-7*c(-1,1); pg <- pgamma(x, shape = 2^-64, lower.tail=FALSE) |
| > stopifnot(qgamma(.99, .00001) == 0, |
| + abs(pg[2] - 1.18928249197237758088243e-20) < 1e-33, |
| + abs(diff(pg) + diff(x)*dgamma(1, 2^-64)) < 1e-13 * mean(pg), |
| + abs(1 - p.1c/1e-100) < 10e-13,# max = 2.243e-13 / 2.442 e-13 |
| + abs(1 - p.3c/1e-300) < 28e-13)# max = 7.057e-13 |
| > ## qgamma() was wrong here, orders of magnitude up to R 2.10.0 |
| > ## pgamma() had inaccuracies, e.g., |
| > ## pgamma(x, shape = 2^-64, lower.tail=FALSE) was discontinuous at x=1 |
| > |
| > stopifnot(all(qpois((0:8)/8, lambda=0) == 0)) |
| > ## gave Inf as p==1 was checked *before* lambda==0 |
| > |
| > ## extreme tail of non-central chisquare |
| > stopifnot(all.equal(pchisq(200, 4, ncp=.001, log.p=TRUE), -3.851e-42)) |
| > ## jumped to zero too early up to R 2.10.1 (PR#14216) |
| > ## left "extreme tail" |
| > lp <- pchisq(2^-(0:200), 100, 1, log=TRUE) |
| > stopifnot(is.finite(lp), lp < -184, |
| + all.equal(lp[201], -7115.10693158)) |
| > dlp <- diff(lp) |
| > dd <- abs(dlp[-(1:30)] - -34.65735902799) |
| > stopifnot(-34.66 < dlp, dlp < -34.41, dd < 1e-8)# 2.2e-10 64bit Lnx |
| > ## underflowed to -Inf much too early in R <= 3.1.0 |
| > for(e in c(0, 2e-16))# continuity at 80 (= branch point) |
| + stopifnot(all.equal(pchisq(1:2, 1.01, ncp = 80*(1-e), log=TRUE), |
| + c(-34.57369629, -31.31514671))) |
| > |
| > ## logit() == qlogit() on the right extreme: |
| > x <- c(10:80, 80 + 5*(1:24), 200 + 20*(1:25)) |
| > stopifnot(All.eq(x, qlogis(plogis(x, log.p=TRUE), |
| + log.p=TRUE))) |
| > ## qlogis() gave Inf much too early for R <= 2.12.1 |
| > ## Part 2: |
| > x <- c(x, seq(700, 800, by=10)) |
| > stopifnot(All.eq(x, qlogis(plogis(x, lower=FALSE, log.p=TRUE), |
| + lower=FALSE, log.p=TRUE))) |
| > # plogis() underflowed to -Inf too early for R <= 2.15.0 |
| > |
| > ## log upper tail pbeta(): |
| > x <- (25:50)/128 |
| > pbx <- pbeta(x, 1/2, 2200, lower.tail=FALSE, log.p=TRUE) |
| > d2p <- diff(dp <- diff(pbx)) |
| > b <- 2200*2^(0:50) |
| > y <- log(-pbeta(.28, 1/2, b, lower.tail=FALSE, log.p=TRUE)) |
| > stopifnot(-1094 < pbx, pbx < -481.66, |
| + -29 < dp, dp < -20, |
| + -.36 < d2p, d2p < -.2, |
| + all.equal(log(b), y+1.113, tolerance = .00002) |
| + ) |
| > ## pbx had two -Inf; y was all Inf for R <= 2.15.3; PR#15162 |
| > |
| > ## dnorm(x) for "large" |x| |
| > stopifnot(abs(1 - dnorm(35+3^-9)/ 3.933395747534971e-267) < 1e-15) |
| > ## has been losing up to 8 bit precision for R <= 3.0.x |
| > |
| > ## pbeta(x, <small a>,<small b>, .., log): |
| > ldp <- diff(log(diff(pbeta(0.5, 2^-(90+ 1:25), 2^-60, log.p=TRUE)))) |
| > stopifnot(abs(ldp - log(1/2)) < 1e-9) |
| > ## pbeta(*, log) lost all precision here, for R <= 3.0.x (PR#15641) |
| > ## |
| > ## "stair function" effect (from denormalized numbers) |
| > a <- 43779; b <- 0.06728 |
| > x. <- .9833 + (0:100)*1e-6 |
| > px <- pbeta(x., a,b, log=TRUE) # plot(x., px) # -> "stair" |
| > d2. <- diff(dpx <- diff(px)) |
| > stopifnot(all.equal(px[1], -746.0986886924, tol=1e-12), |
| + 0.0445741 < dpx, dpx < 0.0445783, |
| + -4.2e-8 < d2., d2. < -4.18e-8) |
| > ## were way off in R <= 3.1.0 |
| > |
| > c0 <- system.time(p0 <- pbeta( .9999, 1e30, 1.001, log=TRUE)) |
| > cB <- max(.001, c0[[1]])# base time |
| > c1 <- system.time(p1 <- pbeta(1- 1e-9, 1e30, 1.001, log=TRUE)) |
| > c2 <- system.time(p2 <- pbeta(1-1e-12, 1e30, 1.001, log=TRUE)) |
| > stopifnot(all.equal(p0, -1.000050003333e26, tol=1e-10), |
| + all.equal(p1, -1e21, tol = 1e-6), |
| + all.equal(p2, -9.9997788e17), |
| + c(c1[[1]], c2[[1]]) < 1000*cB) |
| > ## (almost?) infinite loop in R <= 3.1.0 |
| > |
| > |
| > ## pbinom(), dbinom(), dhyper(),.. : R allows "almost integer" n |
| > for (FUN in c(function(n) dbinom(1,n,0.5), function(n) pbinom(1,n,0.5), |
| + function(n) dpois(n, n), function(n) dhyper(n+1, n+5,n+5, n))) |
| + try( lapply(sample(10000, size=1000), function(M) { |
| + ## invisible(lapply(sample(10000, size=1000), function(M) { |
| + n <- (M/100)*10^(2:20); if(anyNA(P <- FUN(n))) |
| + stop("NA for M=",M, "; 10ex=",paste((2:20)[is.na(P)], collapse=", "))})) |
| > ## check was too tight for large n in R <= 3.1.0 (PR#15734) |
| > |
| > ## [dpqr]beta(*, a,b) where a and/or b are Inf |
| > stopifnot(pbeta(.1, Inf, 40) == 0, |
| + pbeta(.5, 40, Inf) == 1, |
| + pbeta(.4, Inf,Inf) == 0, |
| + pbeta(.5, Inf,Inf) == 1, |
| + ## gave infinite loop (or NaN) in R <= 3.1.0 |
| + qbeta(.9, Inf, 100) == 1, # Inf.loop |
| + qbeta(.1, Inf, Inf) == 1/2)# NaN + Warning |
| > ## range check (in "close" cases): |
| > assertWarning(qN <- qbeta(2^-(10^(1:3)), 2,3, log.p=TRUE)) |
| > assertWarning(qn <- qbeta(c(-.1, -1e-300, 1.25), 2,3)) |
| > stopifnot(is.nan(qN), is.nan(qn)) |
| > |
| > ## lognormal boundary case sdlog = 0: |
| > p <- (0:8)/8; x <- 2^(-10:10) |
| > stopifnot(all.equal(qlnorm(p, meanlog=1:2, sdlog=0), |
| + qlnorm(p, meanlog=1:2, sdlog=1e-200)), |
| + dlnorm(x, sdlog=0) == ifelse(x == 1, Inf, 0)) |
| > |
| > ## qbeta(*, a,b) when a,b << 1 : can easily fail |
| > qbeta(2^-28, 0.125, 2^-26) # 1000 Newton it + warning |
| [1] 9.094955e-13 |
| > a <- 1/8; b <- 2^-(4:200); alpha <- b/4 |
| > qq <- qbeta(alpha, a,b)# gave warnings intermediately |
| > pp <- pbeta(qq, a,b) |
| > stopifnot(pp > 0, diff(pp) < 0, ## pbeta(qbeta(alpha,*),*) == alpha: |
| + abs(1 - pp/alpha) < 4e-15)# seeing 2.2e-16 |
| > |
| > ## orig. qbeta() using *many* Newton steps; case where we "know the truth" |
| > a <- 25; b <- 6; x <- 2^-c(3:15, 100, 200, 250, 300+100*(0:7)) |
| > pb <- c(## via Rmpfr's roundMpfr(pbetaI(x, a,b, log.p=TRUE, precBits = 2048), 64) : |
| + -40.7588797271766572448, -57.7574063441183625303, -74.9287878018119846216, |
| + -92.1806244636893542185, -109.471318248524419364, -126.781111923947395655, |
| + -144.100375042814531426, -161.424352961544612370, -178.750683324909148353, |
| + -196.078188674895169383, -213.406281209657976525, -230.734667259724367416, |
| + -248.063200048177428608, -1721.00081201679567511, -3453.86876341665894863, |
| + -4320.30273911659058550, -5186.73671481652222237, -6919.60466621638549567, |
| + -8652.47261761624876897, -10385.3405690161120427, -12118.2085204159753165, |
| + -13851.0764718158385902, -15583.9444232157018631, -17316.8123746155651368) |
| > stopifnot(all.equal(pb, pbeta(x,a,b, log.p=TRUE), tol=8e-16))# seeing {1.5|1.6|2.0}e-16 |
| > qp <- qbeta(pb, a,b, log.p=TRUE) |
| > ## x == qbeta(pbeta(x, *), *) : |
| > stopifnot(qp > 0, all.equal(x, qp, tol= 1e-15))# seeing {2.4|3.3}e-16 |
| > |
| > ## qbeta(), PR#15755 |
| > a1 <- 0.0672788; b1 <- 226390 |
| > p <- 0.6948886 |
| > qp <- qbeta(p, a1,b1) |
| > stopifnot(qp < 2e-8, # was '1' (with a warning) in R <= 3.1.0 |
| + All.eq(p, pbeta(qp, a1,b1))) |
| > ## less extreme example, same phenomenon: |
| > a <- 43779; b <- 0.06728 |
| > stopifnot(All.eq(0.695, pbeta(qbeta(0.695, b,a), b,a))) |
| > x <- -exp(seq(0, 14, by=2^-9)) |
| > ct <- system.time(qx <- qbeta(x, a,b, log.p=TRUE))[[1]] |
| > pqx <- pbeta(qx, a,b, log=TRUE) |
| > stopifnot(all.equal(x, pqx, tol= 2e-15)) # seeing {3.51|3.54}e-16 |
| > ## note that qx[x > -exp(2)] is too close to 1 to get full accuracy: |
| > ## i2 <- x > -exp(2); all.equal(x[i2], pqx[i2], tol= 0)#-> 5.849e-12 |
| > if(ct > 0.5) { cat("system.time:\n"); print(ct) }# lynne(2013): 0.048 |
| > ## was Inf, and much slower, for R <= 3.1.0 |
| > x3 <- -(15450:15700)/2^11 |
| > pq3 <- pbeta(qbeta(x3, a,b, log.p=TRUE), a,b, log=TRUE) |
| > stopifnot(mean(abs(pq3-x3)) < 4e-12,# 1.46e-12 |
| + max (abs(pq3-x3)) < 8e-12)# 2.95e-12 |
| > ## |
| > .a <- .2; .b <- .03; lp <- -(10^-(1:323)) |
| > qq <- qbeta(lp, .a,.b, log=TRUE) # warnings in R <= 3.1.0 |
| > assertWarning(qN <- qbeta(.5, 2,3, log.p=TRUE)) |
| > assertWarning(qn <- qbeta(c(-.1, 1.25), 2,3)) |
| > stopifnot(1-qq < 1e-15, is.nan(qN), is.nan(qn))# typically qq == 1 exactly |
| > ## failed in intermediate versions |
| > ## |
| > a <- 2^-8; b <- 2^(200:500) |
| > pq <- pbeta(qbeta(1/8, a, b), a, b) |
| > stopifnot(abs(pq - 1/8) < 1/8) |
| > ## whereas qbeta() would underflow to 0 "too early", for R <= 3.1.0 |
| > # |
| > ## very extreme tails on both sides |
| > x <- c(1e-300, 1e-12, 1e-5, 0.1, 0.21, 0.3) |
| > stopifnot(0 == qbeta(x, 2^-12, 2^-10))## gave warnings |
| > a <- 10^-(8:323) |
| > qb <- qbeta(0.95, a, 20) |
| > ## had warnings and wrong value +1; also NaN |
| > ct2 <- system.time(q2 <- qbeta(0.95, a,a))[1] |
| > stopifnot(is.finite(qb), qb < 1e-300, q2 == 1) |
| > if(ct2 > 0.020) { cat("system.time:\n"); print(ct2) } |
| > ## had warnings and was much slower for R <= 3.1.0 |
| > |
| > ## qt(p, df= Inf, ncp) <==> qnorm(p, m=ncp) |
| > p <- (0:32)/32 |
| > stopifnot(all.equal(qt(p, df=Inf, ncp=5), qnorm(p, m=5))) |
| > ## qt(*, df=Inf, .) gave NaN in R <= 3.2.1 |
| > |
| > ## rhyper(*, <large>); PR#16489 |
| > ct3 <- system.time(N <- rhyper(100, 8000, 1e9-8000, 1e6))[1] |
| > table(N) |
| N |
| 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| 1 1 2 2 8 21 9 18 15 10 1 7 1 2 2 |
| > summary(N) |
| Min. 1st Qu. Median Mean 3rd Qu. Max. |
| 0.0 6.0 8.0 7.9 9.0 15.0 |
| > stopifnot(abs(mean(N) - 8) < 1.5) |
| > if(ct3 > 0.02) { cat("system.time:\n"); print(ct3) } |
| > ## N were all 0 and took very long for R <= 3.2.1 |
| > set.seed(17) |
| > stopifnot(rhyper(1, 3024, 27466, 251) == 25, |
| + rhyper(1, 329, 3059, 225) == 22) |
| > ## failed for a day after a "thinko" in the above bug fix. |
| > |
| > ## *chisq(*, df=0, ncp=0) == Point mass at 0 |
| > stopifnot(rchisq(32, df=0, ncp=0) == 0, |
| + dchisq((0:16)/16, df=0, ncp=0) == c(Inf, rep(0, 16))) |
| > ## gave all NaN's for R <= 3.2.2 |
| > |
| > ## pchisq(*, df=0, ncp > 0, log.p=TRUE) : |
| > th <- 10*c(1:9,10^c(1:3,7)) |
| > pp <- pchisq(0, df = 0, ncp=th, log.p=TRUE) |
| > stopifnot(all.equal(pp, -th/2, tol=1e-15)) |
| > ## underflowed at about th ~= 60 in R <= 3.2.2 |
| > |
| > ## pnbinom (-> C's bratio()) |
| > op <- options(warn = 1)# -- NaN's giving warnings |
| > L <- 1e308; p <- suppressWarnings(pnbinom(L, L, mu = 5)) # NaN or 1 (for 64 / 32 bit) |
| > is.nan(p) || p == 1 |
| [1] TRUE |
| > ## gave infinite loop on some 64b platforms in R <= 3.2.3 |
| > |
| > ## [dpqr]nbinom(*, mu, size=Inf) -- PR#16727 |
| > L <- 1e308; mu <- 5; pp <- (0:16)/16 |
| > x <- c(0:3, 1e10, 1e100, L, Inf) |
| > (d <- dnbinom(x, mu = mu, size = Inf)) # gave NaN (for 0 and L) |
| [1] 0.006737947 0.033689735 0.084224337 0.140373896 0.000000000 0.000000000 |
| [7] 0.000000000 0.000000000 |
| > (p <- pnbinom(x, mu = mu, size = Inf)) # gave all NaN |
| [1] 0.006737947 0.040427682 0.124652019 0.265025915 1.000000000 1.000000000 |
| [7] 1.000000000 1.000000000 |
| > (q <- qnbinom(pp, mu = mu, size = Inf)) # gave all NaN |
| [1] 0 2 3 3 3 4 4 4 5 5 6 6 6 7 8 9 Inf |
| > set.seed(1); NI <- rnbinom(32, mu = mu, size = Inf)# gave all NaN |
| > set.seed(1); N2 <- rnbinom(32, mu = mu, size = L ) |
| > stopifnot(all.equal(d, dpois(x, mu)), |
| + all.equal(p, ppois(x, mu)), |
| + q == qpois(pp, mu), |
| + identical(NI, N2)) |
| > options(op) |
| > ## size = Inf -- mostly gave NaN in R <= 3.2.3 |
| > |
| > ## qpois(p, *) for invalid 'p' should give NaN -- PR#16972 |
| > stopifnot(is.nan(suppressWarnings(c(qpois(c(-2,3, NaN), 3), qpois(1, 3, log.p=TRUE), |
| + qpois(.5, 0, log.p=TRUE), qpois(c(-1,pi), 0))))) |
| > ## those in the 2nd line gave 0 in R <= 3.3.1 |
| > ## Similar but different for qgeom(): |
| > stopifnot(qgeom((0:8)/8, prob=1) == 0, ## p=1 gave Inf in R <= 3.3.1 |
| + is.nan(suppressWarnings(qgeom(c(-1/4, 1.1), prob=1)))) |
| > |
| > ## all our RNG r<dist>() functions: |
| > ##' catch all: value and warnings or error <-- demo(error.catching) : |
| > tryCatch.W.E <- function(expr) { |
| + W <- NULL |
| + w.handler <- function(w){ # warning handler |
| + W <<- w |
| + invokeRestart("muffleWarning") |
| + } |
| + list(value = withCallingHandlers(tryCatch(expr, error = function(e) e), |
| + warning = w.handler), |
| + warning = W) |
| + } |
| > .stat.ns <- asNamespace("stats") |
| > Ns <- 4 |
| > for(dist in PDQR) { |
| + fn <- paste0("r",dist) |
| + cat(sprintf("%-9s(%d, ..): ", fn, Ns)) |
| + F <- get(fn, envir = .stat.ns) |
| + nArg <- length(fms <- formals(F)) |
| + if(dist %in% c("nbinom", "gamma")) ## cannot specify *both* 'prob' & 'mu' / 'rate' & 'scale' |
| + nArg <- nArg - 1 |
| + nA1 <- nArg - 1 # those beside the first (= 'n' mostly) |
| + expected <- rep(if(dist %in% PDQRinteg) NA_integer_ else NaN, Ns) |
| + for(ia in seq_len(nA1)) { |
| + aa <- rep(list(1), nA1) |
| + aa[[ia]] <- NA |
| + cat(ia,"") |
| + R <- tryCatch.W.E( do.call(F, c(Ns, aa)) ) |
| + if(!inherits(R$warning, "simpleWarning")) cat(" .. did *NOT* give a warning! ") |
| + if(!(identical(R$value, expected))) { ## allow NA/NaN mismatch in these cases for now: |
| + if(!(dist %in% c("beta","f","t") && all(is.na(R$value)))) |
| + cat(" .. not giving expected NA/NaN's ") |
| + } |
| + } |
| + cat(" [Ok]\n") |
| + } |
| rbinom (4, ..): 1 2 [Ok] |
| rgeom (4, ..): 1 [Ok] |
| rhyper (4, ..): 1 2 3 [Ok] |
| rnbinom (4, ..): 1 2 [Ok] |
| rpois (4, ..): 1 [Ok] |
| rsignrank(4, ..): 1 [Ok] |
| rwilcox (4, ..): 1 2 [Ok] |
| rbeta (4, ..): 1 2 3 [Ok] |
| rcauchy (4, ..): 1 2 [Ok] |
| rchisq (4, ..): 1 2 [Ok] |
| rexp (4, ..): 1 [Ok] |
| rf (4, ..): 1 2 3 [Ok] |
| rgamma (4, ..): 1 2 [Ok] |
| rlnorm (4, ..): 1 2 [Ok] |
| rlogis (4, ..): 1 2 [Ok] |
| rnorm (4, ..): 1 2 [Ok] |
| rt (4, ..): 1 2 [Ok] |
| runif (4, ..): 1 2 [Ok] |
| rweibull (4, ..): 1 2 [Ok] |
| > |
| > |
| > ## qbeta() in very asymmetric cases |
| > sh2 <- 2^seq(9,16, by=1/16) |
| > qbet <- qbeta(1e-10, 1.5, shape2=sh2, lower.tail=FALSE) |
| > plot(sh2, 1- pbeta(qbet, 1.5, sh2, lower.tail=FALSE) * 1e10, log="x") |
| > dqb <- diff(qbet); d2qb <- diff(dqb); d3qb <- diff(d2qb) |
| > stopifnot(all.equal(qbet[[1]], 0.047206901483498, tol=1e-12), |
| + max(abs(1- pbeta(qbet, 1.5, sh2, lower.tail=FALSE) * 1e10)) < 1e-12,# Lx 64b: 2.4e-13 |
| + 0 > dqb, dqb > -0.002, |
| + 0 < d2qb, d2qb < 0.00427, |
| + -3.2e-8 > d3qb, d3qb > -3.1e-6, |
| + diff(d3qb) > 1e-9) |
| > ## had discontinuity (from wrong jump out of Newton) in R <= 3.3.2 |
| > |
| > |
| > ## rt() [PR#17306]; rf() and rbeta() [PR#17375] with non-scalar 'ncp' |
| > nc <- c(NA, 1); iN <- is.na(rep_len(nc, 3)) |
| > ## each gives warning "NAs produced": |
| > assertWarning(T <- rt (3, 4, ncp = nc)) |
| > assertWarning(F <- rf (3, 4,5, ncp = nc)) |
| > assertWarning(B <- rbeta(3, 4,5, ncp = nc)) |
| > stopifnot(identical(iN, is.na(T)), identical(iN, is.na(F)), identical(iN, is.na(B))) |
| > ## was not handled correctly, notably with NA's in ncp, in R <= 3.4.(2|3) |
| > |
| > |
| > ## check old version of walker_Probsample is being used for old sample kind |
| > suppressWarnings(RNGversion("3.5.0")) |
| > set.seed(12345) |
| > p <- c(2, rep(1, 200)) |
| > x <- sample(length(p), 100000, prob = p, replace = TRUE) |
| > stopifnot(sum(x == 1) == 994) |
| > |
| > ## check for faiure of new walker_Probsample |
| > RNGversion("3.6.0") |
| > set.seed(12345) |
| > epsilon <- 1e-10 |
| > p201 <- prop.table( rep( c(1, epsilon), c(201, 999-201))) |
| > x <- sample(length(p201), 100000, prob = p201, replace = TRUE) |
| > stopifnot(sum(x <= 201) == 100000) |
| > |
| > |
| > cat("Time elapsed: ", proc.time() - .ptime,"\n") |
| Time elapsed: 1.522 0.014 1.542 0 0 |
| > |
