Rmpfr (version 0.9-5)

mpfr-distr-etc: Distribution Functions with MPFR Arithmetic

Description

For some R standard (probability) density, distribution or quantile functions, we provide MPFR versions.

Usage

dpois (x, lambda, log = FALSE, useLog = )
dbinom (x, size, prob,     log = FALSE, useLog = )
dnbinom(x, size, prob, mu, log = FALSE, useLog = any(x > 1e6))
dnorm (x, mean = 0, sd = 1, log = FALSE)
dgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
dt (x, df, ncp, log = FALSE)
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)

Value

A vector of the same length as the longest of x,q, ..., of class mpfr with the high accuracy results of the corresponding standard R function.

Arguments

x,q, lambda, size,prob, mu, mean,sd, shape,rate,scale, df,ncp

numeric or mpfr vectors. All of these are “recycled” to the length of the longest one. For their meaning/definition, see the corresponding standard R (stats package) function.

log, log.p, lower.tail

logical, see pnorm, dpois, etc.

useLog

logical with default depending on x etc, indicating if log-scale computation should be used even when log = FALSE, for performance or against overflow / underflow.

Details

pnorm() is based on erf() and erfc() which have direct MPFR counter parts and are both reparametrizations of pnorm, erf(x) = 2*pnorm(sqrt(2)*x) and erfc(x) = 2* pnorm(sqrt(2)*x, lower=FALSE).

See Also

pnorm, dt, dbinom, dnbinom, dgamma, dpois in standard package stats.

pbetaI(x, a,b) is a mpfr version of pbeta only for integer a and b.

Examples

x <- 1400+ 0:10
print(dpois(x, 1000), digits =18) ## standard R's double precision
(px <- dpois(mpfr(x, 120), 1000))## more accuracy for the same
px. <- dpois(mpfr(x, 120), 1000, useLog=TRUE)# {failed in 0.8-8}
stopifnot(all.equal(px, px., tol = 1e-31))
dpois(0:5, mpfr(10000, 80)) ## very small exponents (underflowing in dbl.prec.)

print(dbinom(0:8, 8, pr = 4 / 5), digits=18)
      dbinom(0:8, 8, pr = 4/mpfr(5, 99)) -> dB; dB

print(dnorm(     -5:5), digits=18)
      dnorm(mpfr(-5:5, prec=99))

## For pnorm() in the extreme tails, need an exponent range
## larger than the (MPFR and Rmpfr) default:
(old_eranges <- .mpfr_erange()) # typically -/+ 2^30:
log2(abs(old_eranges))   # 30  30
.mpfr_erange_set(value = (1-2^-52)*.mpfr_erange(c("min.emin","max.emax")))
log2(abs(.mpfr_erange()))# 62  62  *if* setup -- 2023-01: *not* on Winbuilder, nor
## other Windows where long is 4 bytes (32 bit) and the erange typically cannot be extended.
tens <- mpfr(10^(4:7), 128)
pnorm(tens, lower.tail=FALSE, log.p=TRUE) # "works" (iff ...)
## "the" boundary:
pnorm(mpfr(- 38581.371, 128), log.p=TRUE) # still does not underflow {but *.372 does}
## -744261105.599283824811986753129188937418  (iff ...)
.mpfr_erange()*log(2) # the boundary
##          Emin          Emax
## -3.196577e+18  3.196577e+18 (iff ...)

## reset to previous
.mpfr_erange_set( , old_eranges)
pnorm(tens, lower.tail=FALSE, log.p=TRUE) # all but first underflow to -Inf