#### d|ensity #### p|robability (cumulative) #### q|uantile #### r|andom number generation #### #### Functions for ``d/p/q/r'' .ptime <- proc.time() F <- FALSE T <- TRUE ###-- 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 = .Options$rErr.eps) { if(is.null(eps)) { eps <- 1e-30; options(rErr.eps = eps) } ifelse(Mod(true) >= eps, 1 - approx / true, # relative error true - approx) # absolute error (e.g. when true=0) } ## Numerical equality: Here want "rel.error" almost always: All.eq <- function(x,y) all.equal.numeric(x,y, tolerance= 64*.Machine$double.eps, scale = {r <- mean(abs(x),na.rm=TRUE) if(r > 0) r else 0}) if(!interactive()) .Random.seed <- c(0,rep(7654, 3)) ## 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)) { cat("n=",n,": ") for(p in c(0,1,rbeta(n2, 2,4))) { cat(".") 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: tst1 <- all.equal( pbinom(0:k, size = n, prob = p), cumsum(dbinom(0:k, size = n, prob = p))) tst <- 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))) if(!isTRUE(tst1) || !isTRUE(tst)) { cat("n=", n,"; p =",format(p),". k =",k) if(!isTRUE(tst1)) cat("; tst1=",tst1) if(!isTRUE(tst )) cat("; tst=", tst) cat("\n") } } } cat("\n") } ##__ 2. Geometric __ for(pr in seq(0,1,len=15)) { print(All.eq((dg <- dgeom(0:10, pr)), pr * (1-pr)^(0:10))) print(All.eq(cumsum(dg), pgeom(0:10, pr))) } ##__ 3. Hypergeometric __ m <- 10; n <- 7 for(k in 2:m) { x <- 0:(k+1) print(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)) print(all.equal(cumsum(dnbinom(0:7, size, .5)), pnbinom(0:7, size, .5))) All.eq(pnbinom(c(1,3), .9, .5), c(0.777035760338812, 0.946945347071519)) ##__ 5. Poisson __ all(dpois(0:5,0) == c(1, rep(0,5))) all(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)) { tst <- all.equal(1 - pchisq(2*lambda, 2*(1+ 0:k)), pp <- cumsum(dpois(0:k, lambda=lambda)), tol= 100*Meps) if(!isTRUE(tst)) cat("lambda=", format(lambda),". k =",k, " --> tst=", tst,"\n") tst2 <- all.equal(pp, ppois(0:k, lambda=lambda), tol = 100*Meps) if(!isTRUE(tst2)) cat("lambda=", format(lambda),". k =",k, " --> tst2=", tst2,"\n") tst3 <- all.equal(1 - pp, ppois(0:k, lambda=lambda, lower.tail=FALSE)) if(!isTRUE(tst3)) cat("lambda=", format(lambda),". k =",k, " --> tst3=", tst3,"\n") } ##__ 6. SignRank __ for(n in rpois(32, lam=8)) { x <- -1:(n + 4) if(!isTRUE(eq <- All.eq(psignrank(x, n), cumsum(dsignrank(x, n))))) print(eq) } ##__ 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)) if(!isTRUE(eq <- All.eq(Fx, cumsum(fx)))) print(eq) } 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)) { tst <- all.equal((d1 <- dgamma( x, shape = sh, scale = sig)), (d2 <- dgamma(x/sig, shape = sh, scale = 1) / sig), tol = 1e-14)## __ad interim__ was 1e-15 if(!isTRUE(tst)) cat("ERROR: dgamma() doesn't scale:",tst,"\n", " x =", formatC(x),"\n shape,scale=",formatC(c(sh, sig)),"\n") tst <- All.eq(d1, (d3 <- 1/(Ga * sig^sh) * x^(sh-1) * exp(-x/sig))) if(!isTRUE(tst)) cat("NOT Equal:",tst,"\n x =", formatC(x), "\n shape,scale=",formatC(c(sh, sig)),"\n") } } pgamma(1,Inf,scale=Inf) == 0 ## Also pgamma(Inf,Inf) == 1 for which NaN was slightly more appropriate all(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), tol=2e-15) ) p <- 7e-4; df <- 0.9 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(log(1-p),df,log=T,lower=F),df, log=T,lower=F)/log(1-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) all.equal(qchisq(0.025,31,ncp=1,lower.tail=FALSE),# inf.loop PR#875 49.7766246561514, tol= 1e-11) for(df in c(0.1, 0.5, 1.5, 4.7, 10, 20,50,100)) { cat("df =", formatC(df, wid=3)) 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) print(all.equal(xx, qchisq(pp, df=df, ncp=1), tol = dtol))# TRUE ##or print(mapply(rErr, xx, qchisq(pp, df=df,ncp=1)), digits = 3) } ## 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) p0 <- pchisq(q0, df=1.2, ncp=10, lower.tail=FALSE) p1 <- pchisq(q1, df=1.2, ncp=10, lower.tail=FALSE) iO <- 1:10 all.equal(q0[iO], q1[iO]) all.equal(p0[iO], psml[iO], tol = 0.08)# bad tol (0.0744 on 386-Linux). ##--- Beta (need more): ## big a & b (PR #643) summary(a <- rlnorm(20, 5.5)) summary(b <- rlnorm(20, 6.5)) pab <- expand.grid(seq(0,1,by=.1), a, b) p <- pab[,1]; a <- pab[,2]; b <- pab[,3] all.equal(dbeta(p,a,b), exp(pab <- dbeta(p,a,b, log = TRUE)), tol = 1e-11) sample(pab, 50) ##--- Normal (& Lognormal) : qnorm(0) == -Inf && qnorm(-Inf, log = TRUE) == -Inf qnorm(1) == Inf && qnorm(0, log = TRUE) == Inf is.nan(qnorm(1.1)) && is.nan(qnorm(-.1)) # + warn x <- c(-Inf, -1e100, 1:6, 1e200, Inf) rbind(d.s0 =dnorm(x,3,s=0), p.s0 = pnorm(x,3,s=0), d.sI =dnorm(x,3,s=Inf), p.sI = pnorm(x,3,s=Inf)) ## 3 Test data from Wichura (1988) : all.equal(qnorm(c( 0.25, .001, 1e-20)), c(-0.6744897501960817, -3.090232306167814, -9.262340089798408), tol = 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), tol= 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) if(!isTRUE(all.equal(pt(z, df), 1 - pt(-z,df), tol= 1e-15))) cat("ERROR -- df = ", df, "\n") 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 norm 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]), tol= 1e-12) ###===== Random numbers -- first, just output: .Random.seed <- c(0, 17292, 29447, 24113) n <- 20 ## for(pre in PDQR) { n <- paste("r",pre,sep=""); cat(n,": "); str(get(n))} (Rbeta <- rbeta (n, shape1 = .8, shape2 = 2) ) (Rbinom <- 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 <- rgeom (n, prob = pi/16) ) (Rhyper <- 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 <- 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*(.)) = identity All.eq(Rbeta, qbeta (Pbeta, shape1 = .8, shape2 = 2)) All.eq(Rbinom, qbinom (Pbinom, 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, prob = pi/16)) All.eq(Rhyper, qhyper (Phyper, 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, size = 7, prob = .01)) All.eq(Rnorm, qnorm (Pnorm, mean = -1, sd = 3)) All.eq(Rpois, qpois (Ppois, lambda = 12)) All.eq(Rsignrank, qsignrank(Psignrank, n = 47)) All.eq(Rt, qt (Pt, df = 11)) all.equal(Rt2, qt (Pt2, df = 1.01), tol = 1e-2) All.eq(Runif, qunif (Punif, min = .2, max = 2)) All.eq(Rweibull, qweibull (Pweibull, shape = 3, scale = 2)) All.eq(Rwilcox, qwilcox (Pwilcox, m = 13, n = 17)) ## Same with "upper tail": All.eq(Rbeta, qbeta (1- Pbeta, shape1 = .8, shape2 = 2, lower=F)) All.eq(Rbinom, qbinom (1- 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 (1- Pgeom, prob = pi/16, lower=F)) All.eq(Rhyper, qhyper (1- 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 (1- Pnbinom, size = 7, prob = .01, lower=F)) All.eq(Rnorm, qnorm (1- Pnorm, mean = -1, sd = 3,lower=F)) All.eq(Rpois, qpois (1- Ppois, lambda = 12, lower=F)) All.eq(Rsignrank, qsignrank(1- Psignrank, n = 47, lower=F)) All.eq(Rt, qt (1- Pt, df = 11, lower=F)) all.equal(Rt2, qt (1- Pt2, df = 1.01, lower=F), tol = 1e-2) 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 (1- Pwilcox, m = 13, n = 17, lower=F)) ## Check q*(p* ( log ), log) = identity All.eq(Rbeta, qbeta (log(Pbeta), shape1 = .8, shape2 = 2, log=TRUE)) All.eq(Rbinom, qbinom (log(Pbinom), size = 55, prob = pi/16, log=TRUE)) All.eq(Rcauchy, qcauchy (log(Pcauchy), location = 12, scale = 2, log=TRUE)) all.equal(Rchisq, qchisq (log(Pchisq), df = 3, log=TRUE),tol=1e-14) 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), prob = pi/16, log=TRUE)) All.eq(Rhyper, qhyper (log(Phyper), 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), size = 7, prob = .01, log=TRUE)) All.eq(Rnorm, qnorm (log(Pnorm), mean = -1, sd = 3, log=TRUE)) All.eq(Rpois, qpois (log(Ppois), lambda = 12, log=TRUE)) All.eq(Rsignrank, qsignrank(log(Psignrank), n = 47, log=TRUE)) All.eq(Rt, qt (log(Pt), df = 11, log=TRUE)) all.equal(Rt2, qt (log(Pt2), df = 1.01, log=TRUE), tol = 1e-2) 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), m = 13, n = 17, log=TRUE)) ## same q*(p* (log) log) with upper tail: All.eq(Rbeta, qbeta (log(1- Pbeta), shape1 = .8, shape2 = 2, lower=F, log=T)) All.eq(Rbinom, qbinom (log(1- Pbinom), size = 55, prob = pi/16, lower=F, log=T)) All.eq(Rcauchy, qcauchy (log(1- Pcauchy), location = 12, scale = 2, lower=F, log=T)) All.eq(Rchisq, qchisq (log(1- Pchisq), df = 3, lower=F, log=T)) All.eq(Rexp, qexp (log(1- Pexp), rate = 2, lower=F, log=T)) All.eq(Rf, qf (log(1- Pf), df1 = 12, df2 = 6, lower=F, log=T)) All.eq(Rgamma, qgamma (log(1- Pgamma), shape = 2, scale = 5, lower=F, log=T)) All.eq(Rgeom, qgeom (log(1- Pgeom), prob = pi/16, lower=F, log=T)) All.eq(Rhyper, qhyper (log(1- Phyper), m = 40, n = 30, k = 20, lower=F, log=T)) All.eq(Rlnorm, qlnorm (log(1- Plnorm), meanlog = -1, sdlog = 3, lower=F, log=T)) All.eq(Rlogis, qlogis (log(1- Plogis), location = 12, scale = 2, lower=F, log=T)) All.eq(Rnbinom, qnbinom (log(1- Pnbinom), size = 7, prob = .01, lower=F, log=T)) All.eq(Rnorm, qnorm (log(1- Pnorm), mean = -1, sd = 3, lower=F, log=T)) All.eq(Rpois, qpois (log(1- Ppois), lambda = 12, lower=F, log=T)) All.eq(Rsignrank, qsignrank(log(1- Psignrank), n = 47, lower=F, log=T)) All.eq(Rt, qt (log(1- Pt ), df = 11, lower=F, log=T)) all.equal(Rt2, qt (log(1- Pt2), df = 1.01, lower=F, log=T), tol = 1e-2) All.eq(Runif, qunif (log(1- Punif), min = .2, max = 2, lower=F, log=T)) All.eq(Rweibull, qweibull (log(1- Pweibull), shape = 3, scale = 2, lower=F, log=T)) All.eq(Rwilcox, qwilcox (log(1- Pwilcox), m = 13, n = 17, lower=F, log=T)) ## Check log( upper.tail ): All.eq(log(1 - Pbeta), pbeta (Rbeta, shape1 = .8, shape2 = 2, lower=F, log=T)) All.eq(log(1 - Pbinom), pbinom (Rbinom, size = 55, prob = pi/16, lower=F, log=T)) All.eq(log(1 - Pcauchy), pcauchy (Rcauchy, location = 12, scale = 2, lower=F, log=T)) All.eq(log(1 - Pchisq), pchisq (Rchisq, df = 3, lower=F, log=T)) All.eq(log(1 - Pexp), pexp (Rexp, rate = 2, lower=F, log=T)) All.eq(log(1 - Pf), pf (Rf, df1 = 12, df2 = 6, lower=F, log=T)) All.eq(log(1 - Pgamma), pgamma (Rgamma, shape = 2, scale = 5, lower=F, log=T)) All.eq(log(1 - Pgeom), pgeom (Rgeom, prob = pi/16, lower=F, log=T)) All.eq(log(1 - Phyper), phyper (Rhyper, m = 40, n = 30, k = 20, lower=F, log=T)) All.eq(log(1 - Plnorm), plnorm (Rlnorm, meanlog = -1, sdlog = 3, lower=F, log=T)) All.eq(log(1 - Plogis), plogis (Rlogis, location = 12, scale = 2, lower=F, log=T)) All.eq(log(1 - Pnbinom), pnbinom (Rnbinom, size = 7, prob = .01, lower=F, log=T)) All.eq(log(1 - Pnorm), pnorm (Rnorm, mean = -1, sd = 3, lower=F, log=T)) All.eq(log(1 - Ppois), ppois (Rpois, lambda = 12, lower=F, log=T)) All.eq(log(1 - Psignrank), psignrank(Rsignrank, n = 47, lower=F, log=T)) All.eq(log(1 - Pt), pt (Rt, df = 11, lower=F, log=T)) All.eq(log(1 - Pt2), pt (Rt2,df = 1.01, lower=F, log=T)) All.eq(log(1 - Punif), punif (Runif, min = .2, max = 2, lower=F, log=T)) All.eq(log(1 - Pweibull), pweibull (Rweibull, shape = 3, scale = 2, lower=F, log=T)) All.eq(log(1 - Pwilcox), pwilcox (Rwilcox, m = 13, n = 17, lower=F, log=T)) ### (Extreme) tail tests added more recently: All.eq(1, -1e-17/ pexp(qexp(-1e-17, log=TRUE),log=TRUE)) abs(pgamma(30,100, lower=FALSE, log=TRUE) + 7.3384686328784e-24) < 1e-36 All.eq(1, pcauchy(-1e20) / 3.18309886183791e-21) All.eq(1, pcauchy(+1e15, log=TRUE) / -3.18309886183791e-16)## PR#6756 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)) print(all.equal(pt(-a, df=1), pcauchy(-a), tol = 1e-15)) ## for PR#7902: ex <- -c(rev(1/x), ex) All.eq(-x, qcauchy(pcauchy(-x))) All.eq(+x, qcauchy(pcauchy(+x, log=TRUE), log=TRUE)) All.eq(1/x, pcauchy(qcauchy(1/x))) All.eq(ex, pcauchy(qcauchy(ex, log=TRUE), log=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 <- 1e-23 ## PR#6757 stopifnot(all.equal(pr^ 12, pbinom(11, 12, prob= pr,lower=FALSE), tol= 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))) 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)), tol = 1e-12)# 3.984e-14 (i386) all.equal(pgamma(x, 0.1, log = TRUE) - 0.1*log(x), rep(0.0498724412598364, length(x)), tol = 1e-13)# 7e-16 (i386) All.eq(dpois( 10, 2e-308, log=TRUE), -7100.13502718914) All.eq(dpois( 20, 3e-308, log=TRUE), -14204.2875435307) All.eq(dpois(1e20, 1e-290, log=TRUE), -7.12801378828154e+22) ## 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) 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 2.1.1 pf(x, Inf, Inf)# (0, 1/2, 1) pf(x, 5, Inf, ncp=0) pf(x, 5, 1e6, ncp=1) pf(x, 5, 1e7, ncp=1) all.equal(pf(x, 5, 1e8, ncp=1), tol = 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 options(oo) ## Inf valid as from 2.1.1: df(x, 1e16, 5) was way off in 2.0.1. ## PR#7099 : pf() with large df1 or df2: nu <- 2^seq(25,34, 0.5) y <- 1e9*(pf(1,1,nu) - 0.68268949) stopifnot(All.eq(pf(1,1,Inf), 0.68268949213708596), diff(y) > 0, # i.e. pf(1,1, *) is monotone increasing All.eq(y [1], -5.07420372386491), All.eq(y[19], 2.12300110824515)) ## not at all in R 2.1.0 or earlier 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 cat("Time elapsed: ", proc.time() - .ptime,"\n")