The R Project SVN
R
(root)/branches/R-typeset/tests/d-p-q-r-tests.R – Rev 82735
Rev 80940 | Blame | Compare with Previous | Last modification | View Log | Download | RSS feed
#### d|ensity#### p|robability (cumulative)#### q|uantile#### r|andom number generation######## Functions for ``d/p/q/r''F <- FALSET <- TRUEshowSys.time <- function(expr, ...) {## prepend 'Time' for R CMD Rdiffst <- system.time(expr, ...)writeLines(paste("Time", capture.output(print(st))))invisible(st)}options(warn = 2)## ======== No warnings, unless explicitly asserted viaassertWarning <- tools::assertWarningas.nan <- function(x) { x[is.na(x) & !is.nan(x)] <- NaN ; x }###-- these are identical in ./arith-true.R ["fixme": use source(..)]opt.conformance <- 0Meps <- .Machine $ double.epsxMax <- .Machine $ double.xmaxoptions(rErr.eps = 1e-30)rErr <- function(approx, true, eps = getOption("rErr.eps", 1e-30)){ifelse(Mod(true) >= eps,1 - approx / true, # relative errortrue - 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).ptime <- proc.time()## The prefixes of ALL the PDQ & R functionsPDQRinteg <- 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 <- 8for(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 elsepf((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 distributionstopifnot(All.eq((dg <- dgeom(0:10, pr)),pr * (1-pr)^(0:10)),All.eq(cumsum(dg), pgeom(0:10, pr)))##__ 3. Hypergeometric __.suppHyper <- function(m,n,k) max(0, k-n) : min(k, m)hyp.mn <- rbind(m = c(10, 15, 999),n = c( 7, 0, 0))for(j in 1:ncol(hyp.mn)) {mn <- hyp.mn[,j]; m <- mn[["m"]] ; n <- mn[["n"]]cat("m=",m,"; n=",n,":\n")showSys.time(for(k in 2:m) {x <- .suppHyper(m,n,k); x <- c(x[1]-1L, x)stopifnot(All.eq(phyper(x, m, n, k), cumsum(dhyper(x, m, n, k))))stopifnot(All.eq(phyper(x, m, n, k, log.p=TRUE),log(cumsum(dhyper(x, m, n, k)))))})}##__ 4. Negative Binomial __## PR #842for(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 <- 16for(lambda in rexp(n1))for(k in rpois(n2, lambda))stopifnot(all.equal(pchisq(2*lambda, 2*(1+ 0:k), lower.tail = FALSE),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 <- TRUEfor(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 appropriateassertWarning(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 <- 0.9stopifnot(abs(1-c(pchisq(qchisq(p, df),df)/p, # was 2.31e-8 for R <= 1.8.1pchisq(qchisq(1-p, df,lower=FALSE),df,lower=FALSE)/(1-p),# was 1.618e-11pchisq(qchisq(log(p), df,log=TRUE),df, log=TRUE)/log(p), # was 3.181e-9pchisq(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#87549.7766246561514, 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#6421psml <- 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 tailp0 <- pchisq(q0, df=1.2, ncp=10, lower.tail=FALSE)p1 <- pchisq(q1, df=1.2, ncp=10, lower.tail=FALSE)iO <- 1:30stopifnot(all.equal(q0[iO], q1[iO], tolerance = 1e-5),# 9.86e-8all.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)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 <- 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))## 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 normstopifnot(All.eq(pz, plnorm(exp(z))))###========== p <-> q Inversion consistency =====================ok <- 1e-5 < pz & pz < 1 - 1e-5all.equal(z[ok], qnorm(pz[ok]), tolerance = 1e-12)###===== Random numbers -- first, just output:set.seed(123)n <- 20## for(pre in PDQR) { n <- paste("r",pre,sep=""); cat(n,": "); str(get(n))}(Rbeta <- rbeta (n, shape1 = .8, shape2 = 2) )(Rbinom <- sort(unique(rbinom (n, size = 55, prob = pi/16))))(Rcauchy <- rcauchy (n, location = 12, scale = 2) )(Rchisq <- rchisq (n, df = 3) )(Rexp <- rexp (n, rate = 2) )(Rf <- rf (n, df1 = 12, df2 = 6) )(Rgamma <- rgamma (n, shape = 2, scale = 5) )(Rgeom <- sort(unique(rgeom (n, prob = pi/16))))(Rhyper <- sort(unique(rhyper (n, m = 40, n = 30, k = 20))))(Rlnorm <- rlnorm (n, meanlog = -1, sdlog = 3) )(Rlogis <- rlogis (n, location = 12, scale = 2) )(Rnbinom <- rnbinom (n, size = 7, prob = .01) )(Rnorm <- rnorm (n, mean = -1, sd = 3) )(Rpois <- sort(unique(rpois (n, lambda = 12))))(Rsignrank<- rsignrank(n, n = 47) )(Rt <- rt (n, df = 11) )## Rt2 below (to preserve the following random numbers!)(Runif <- runif (n, min = .2, max = 2) )(Rweibull <- rweibull (n, shape = 3, scale = 2) )(Rwilcox <- rwilcox (n, m = 13, n = 17) )(Rt2 <- rt (n, df = 1.01))(Pbeta <- pbeta (Rbeta, shape1 = .8, shape2 = 2) )(Pbinom <- pbinom (Rbinom, size = 55, prob = pi/16) )(Pcauchy <- pcauchy (Rcauchy, location = 12, scale = 2) )(Pchisq <- pchisq (Rchisq, df = 3) )(Pexp <- pexp (Rexp, rate = 2) )(Pf <- pf (Rf, df1 = 12, df2 = 6) )(Pgamma <- pgamma (Rgamma, shape = 2, scale = 5) )(Pgeom <- pgeom (Rgeom, prob = pi/16) )(Phyper <- phyper (Rhyper, m = 40, n = 30, k = 20) )(Plnorm <- plnorm (Rlnorm, meanlog = -1, sdlog = 3) )(Plogis <- plogis (Rlogis, location = 12, scale = 2) )(Pnbinom <- pnbinom (Rnbinom, size = 7, prob = .01) )(Pnorm <- pnorm (Rnorm, mean = -1, sd = 3) )(Ppois <- ppois (Rpois, lambda = 12) )(Psignrank<- psignrank(Rsignrank, n = 47) )(Pt <- pt (Rt, df = 11) )(Pt2 <- pt (Rt2, df = 1.01) )(Punif <- punif (Runif, min = .2, max = 2) )(Pweibull <- pweibull (Rweibull, shape = 3, scale = 2) )(Pwilcox <- pwilcox (Rwilcox, m = 13, n = 17) )dbeta (Rbeta, shape1 = .8, shape2 = 2)dbinom (Rbinom, size = 55, prob = pi/16)dcauchy (Rcauchy, location = 12, scale = 2)dchisq (Rchisq, df = 3)dexp (Rexp, rate = 2)df (Rf, df1 = 12, df2 = 6)dgamma (Rgamma, shape = 2, scale = 5)dgeom (Rgeom, prob = pi/16)dhyper (Rhyper, m = 40, n = 30, k = 20)dlnorm (Rlnorm, meanlog = -1, sdlog = 3)dlogis (Rlogis, location = 12, scale = 2)dnbinom (Rnbinom, size = 7, prob = .01)dnorm (Rnorm, mean = -1, sd = 3)dpois (Rpois, lambda = 12)dsignrank(Rsignrank, n = 47)dt (Rt, df = 11)dunif (Runif, min = .2, max = 2)dweibull (Rweibull, shape = 3, scale = 2)dwilcox (Rwilcox, m = 13, n = 17)## Check q*(p*(.)) = identityep <- 1e-7f1 <- 1 - 1e-7 # = 0.9999999All.eq(Rbeta, qbeta (Pbeta, shape1 = .8, shape2 = 2))All.eq(Rbinom, qbinom (Pbinom*f1, size = 55, prob = pi/16))All.eq(Rcauchy, qcauchy (Pcauchy, location = 12, scale = 2))All.eq(Rchisq, qchisq (Pchisq, df = 3))All.eq(Rexp, qexp (Pexp, rate = 2))All.eq(Rf, qf (Pf, df1 = 12, df2 = 6))All.eq(Rgamma, qgamma (Pgamma, shape = 2, scale = 5))All.eq(Rgeom, qgeom (Pgeom*f1, prob = pi/16))All.eq(Rhyper, qhyper (Phyper*f1, m = 40, n = 30, k = 20))All.eq(Rlnorm, qlnorm (Plnorm, meanlog = -1, sdlog = 3))All.eq(Rlogis, qlogis (Plogis, location = 12, scale = 2))All.eq(Rnbinom, qnbinom (Pnbinom*f1, size = 7, prob = .01))All.eq(Rnorm, qnorm (Pnorm, mean = -1, sd = 3))All.eq(Rpois, qpois (Ppois*f1, lambda = 12))All.eq(Rsignrank, qsignrank(Psignrank*f1, n = 47))All.eq(Rt, qt (Pt, df = 11))All.eq(Rt2, qt (Pt2, df = 1.01))All.eq(Runif, qunif (Punif, min = .2, max = 2))All.eq(Rweibull, qweibull (Pweibull, shape = 3, scale = 2))All.eq(Rwilcox, qwilcox (Pwilcox*f1, m = 13, n = 17))## Same with "upper tail":p1 <- 1 + epAll.eq(Rbeta, qbeta (1- Pbeta, shape1 = .8, shape2 = 2, lower=F))All.eq(Rbinom, qbinom (p1- Pbinom, size = 55, prob = pi/16, lower=F))All.eq(Rcauchy, qcauchy (1- Pcauchy, location = 12, scale = 2, lower=F))All.eq(Rchisq, qchisq (1- Pchisq, df = 3, lower=F))All.eq(Rexp, qexp (1- Pexp, rate = 2, lower=F))All.eq(Rf, qf (1- Pf, df1 = 12, df2 = 6, lower=F))All.eq(Rgamma, qgamma (1- Pgamma, shape = 2, scale = 5, lower=F))All.eq(Rgeom, qgeom (p1- Pgeom, prob = pi/16, lower=F))All.eq(Rhyper, qhyper (p1- Phyper, m = 40, n = 30, k = 20, lower=F))All.eq(Rlnorm, qlnorm (1- Plnorm, meanlog = -1, sdlog = 3, lower=F))All.eq(Rlogis, qlogis (1- Plogis, location = 12, scale = 2, lower=F))All.eq(Rnbinom, qnbinom (p1- Pnbinom, size = 7, prob = .01, lower=F))All.eq(Rnorm, qnorm (1- Pnorm, mean = -1, sd = 3,lower=F))All.eq(Rpois, qpois (p1- Ppois, lambda = 12, lower=F))All.eq(Rsignrank, qsignrank(p1-Psignrank, n = 47, lower=F))All.eq(Rt, qt (1- Pt, df = 11, lower=F))All.eq(Rt2, qt (1- Pt2, df = 1.01, lower=F))All.eq(Runif, qunif (1- Punif, min = .2, max = 2, lower=F))All.eq(Rweibull, qweibull (1- Pweibull, shape = 3, scale = 2, lower=F))All.eq(Rwilcox, qwilcox (p1- Pwilcox, m = 13, n = 17, lower=F))## Check q*(p* ( log ), log) = identityAll.eq(Rbeta, qbeta (log(Pbeta), shape1 = .8, shape2 = 2, log=TRUE))All.eq(Rbinom, qbinom (log(Pbinom)-ep, size = 55, prob = pi/16, log=TRUE))All.eq(Rcauchy, qcauchy (log(Pcauchy), location = 12, scale = 2, log=TRUE))All.eq(Rchisq, qchisq (log(Pchisq), df = 3, log=TRUE))All.eq(Rexp, qexp (log(Pexp), rate = 2, log=TRUE))All.eq(Rf, qf (log(Pf), df1= 12, df2= 6, log=TRUE))All.eq(Rgamma, qgamma (log(Pgamma), shape = 2, scale = 5, log=TRUE))All.eq(Rgeom, qgeom (log(Pgeom)-ep, prob = pi/16, log=TRUE))All.eq(Rhyper, qhyper (log(Phyper)-ep, m = 40, n = 30, k = 20, log=TRUE))All.eq(Rlnorm, qlnorm (log(Plnorm), meanlog = -1, sdlog = 3, log=TRUE))All.eq(Rlogis, qlogis (log(Plogis), location = 12, scale = 2, log=TRUE))All.eq(Rnbinom, qnbinom (log(Pnbinom)-ep, size = 7, prob = .01, log=TRUE))All.eq(Rnorm, qnorm (log(Pnorm), mean = -1, sd = 3, log=TRUE))All.eq(Rpois, qpois (log(Ppois)-ep, lambda = 12, log=TRUE)) # fuzz for SolarisAll.eq(Rsignrank, qsignrank(log(Psignrank)-ep, n = 47, log=TRUE))All.eq(Rt, qt (log(Pt), df = 11, log=TRUE))All.eq(Rt2, qt (log(Pt2), df = 1.01, log=TRUE))All.eq(Runif, qunif (log(Punif), min = .2, max = 2, log=TRUE))All.eq(Rweibull, qweibull (log(Pweibull), shape = 3, scale = 2, log=TRUE))All.eq(Rwilcox, qwilcox (log(Pwilcox)-ep, m = 13, n = 17, log=TRUE))## same q*(p* (log) log) with upper tail:All.eq(Rbeta, qbeta (log1p(-Pbeta), shape1 = .8, shape2 = 2, lower=F, log=T))All.eq(Rbinom, qbinom (log1p(-Pbinom)+ep, size = 55, prob = pi/16, lower=F, log=T))All.eq(Rcauchy, qcauchy (log1p(-Pcauchy), location = 12, scale = 2, lower=F, log=T))All.eq(Rchisq, qchisq (log1p(-Pchisq), df = 3, lower=F, log=T))All.eq(Rexp, qexp (log1p(-Pexp), rate = 2, lower=F, log=T))All.eq(Rf, qf (log1p(-Pf), df1 = 12, df2 = 6, lower=F, log=T))All.eq(Rgamma, qgamma (log1p(-Pgamma), shape = 2, scale = 5, lower=F, log=T))All.eq(Rgeom, qgeom (log1p(-Pgeom)+ep, prob = pi/16, lower=F, log=T))All.eq(Rhyper, qhyper (log1p(-Phyper)+ep, m = 40, n = 30, k = 20, lower=F, log=T))All.eq(Rlnorm, qlnorm (log1p(-Plnorm), meanlog = -1, sdlog = 3, lower=F, log=T))All.eq(Rlogis, qlogis (log1p(-Plogis), location = 12, scale = 2, lower=F, log=T))All.eq(Rnbinom, qnbinom (log1p(-Pnbinom)+ep, size = 7, prob = .01, lower=F, log=T))All.eq(Rnorm, qnorm (log1p(-Pnorm), mean = -1, sd = 3, lower=F, log=T))All.eq(Rpois, qpois (log1p(-Ppois)+ep, lambda = 12, lower=F, log=T))All.eq(Rsignrank, qsignrank(log1p(-Psignrank)+ep, n = 47, lower=F, log=T))All.eq(Rt, qt (log1p(-Pt ), df = 11, lower=F, log=T))All.eq(Rt2, qt (log1p(-Pt2), df = 1.01, lower=F, log=T))All.eq(Runif, qunif (log1p(-Punif), min = .2, max = 2, lower=F, log=T))All.eq(Rweibull, qweibull (log1p(-Pweibull), shape = 3, scale = 2, lower=F, log=T))All.eq(Rwilcox, qwilcox (log1p(-Pwilcox)+ep, m = 13, n = 17, lower=F, log=T))## Check log( upper.tail ):All.eq(log1p(-Pbeta), pbeta (Rbeta, shape1 = .8, shape2 = 2, lower=F, log=T))All.eq(log1p(-Pbinom), pbinom (Rbinom, size = 55, prob = pi/16, lower=F, log=T))All.eq(log1p(-Pcauchy), pcauchy (Rcauchy, location = 12, scale = 2, lower=F, log=T))All.eq(log1p(-Pchisq), pchisq (Rchisq, df = 3, lower=F, log=T))All.eq(log1p(-Pexp), pexp (Rexp, rate = 2, lower=F, log=T))All.eq(log1p(-Pf), pf (Rf, df1 = 12, df2 = 6, lower=F, log=T))All.eq(log1p(-Pgamma), pgamma (Rgamma, shape = 2, scale = 5, lower=F, log=T))All.eq(log1p(-Pgeom), pgeom (Rgeom, prob = pi/16, lower=F, log=T))All.eq(log1p(-Phyper), phyper (Rhyper, m = 40, n = 30, k = 20, lower=F, log=T))All.eq(log1p(-Plnorm), plnorm (Rlnorm, meanlog = -1, sdlog = 3, lower=F, log=T))All.eq(log1p(-Plogis), plogis (Rlogis, location = 12, scale = 2, lower=F, log=T))All.eq(log1p(-Pnbinom), pnbinom (Rnbinom, size = 7, prob = .01, lower=F, log=T))All.eq(log1p(-Pnorm), pnorm (Rnorm, mean = -1, sd = 3, lower=F, log=T))All.eq(log1p(-Ppois), ppois (Rpois, lambda = 12, lower=F, log=T))All.eq(log1p(-Psignrank), psignrank(Rsignrank, n = 47, lower=F, log=T))All.eq(log1p(-Pt), pt (Rt, df = 11, lower=F, log=T))All.eq(log1p(-Pt2), pt (Rt2,df = 1.01, lower=F, log=T))All.eq(log1p(-Punif), punif (Runif, min = .2, max = 2, lower=F, log=T))All.eq(log1p(-Pweibull), pweibull (Rweibull, shape = 3, scale = 2, lower=F, log=T))All.eq(log1p(-Pwilcox), pwilcox (Rwilcox, m = 13, n = 17, lower=F, log=T))## 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)df(x, 3, Inf)pf(x, 3, 1e6)pf(x, 3, Inf)df(x, 1e6, 5)df(x, Inf, 5)pf(x, 1e6, 5)pf(x, Inf, 5)df(x, Inf, Inf)# (0, Inf, 0) - since 2.1.1pf(x, Inf, Inf)# (0, 1/2, 1)pf(x, 5, Inf, ncp=0)all.equal(pf(x, 5, 1e6, ncp=1), tolerance = 1e-6,c(0.065933194, 0.470879987, 0.978875867))all.equal(pf(x, 5, 1e7, ncp=1), tolerance = 1e-6,c(0.06593309, 0.47088028, 0.97887641))all.equal(pf(x, 5, 1e8, ncp=1), tolerance = 1e-6,c(0.0659330751, 0.4708802996, 0.9788764591))pf(x, 5, Inf, ncp=1)dt(1, Inf)dt(1, Inf, ncp=0)dt(1, Inf, ncp=1)dt(1, 1e6, ncp=1)dt(1, 1e7, ncp=1)dt(1, 1e8, ncp=1)dt(1, 1e10, ncp=1) # = Inf## 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))## small 'x' used to suffer from cancellationoptions(oo)## NB: Do *NOT* add new examples here, but rather in ./d-p-q-r-tst-2.R## == ~~~ ~~~~ ~~~ ~~~~~~~~~~~~~~~cat("Time elapsed: ", proc.time() - .ptime,"\n")