distr-etc: Distribution Functions with MPFR Arithmetic

In Rmpfr: Interface R to MPFR - Multiple Precision Floating-Point Reliable

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)

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).

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.

Note

E.g., for pnorm(*, log.p = TRUE) to be useful, i.e., not to underflow or overflow, you may want to extend the exponential range of MPFR numbers, using .mpfr_erange_set(), see the examples.

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

Rmpfr documentation built on Nov. 18, 2024, 3:01 p.m.