#### d|ensity
#### p|robability (cumulative)
#### q|uantile
#### r|andom number generation
####
#### Functions for ``d/p/q/r''
F <- FALSE
T <- TRUE
showSys.time <- function(expr, ...) {
## prepend 'Time' for R CMD Rdiff
st <- system.time(expr, ...)
writeLines(paste("Time", capture.output(print(st))))
invisible(st)
}
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)
.ptime <- proc.time()
## 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 __
.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 #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(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 <- 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))
stopifnot(
## 3 Test data from Wichura (1988) :
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(qe5 <- qnorm(-1e5, log = TRUE), -447.1978937)
, ## much more accurate (2022-08):
All.eq(-1e5, pnorm(qe5, log = TRUE))
)
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 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)
###===== 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*(.)) = identity
ep <- 1e-7
f1 <- 1 - 1e-7 # = 0.9999999
All.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 + ep
All.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) = identity
All.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 Solaris
All.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 2.1.1
pf(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 cancellation
options(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")