Distribution Functions etc (MPFR)
For some R standard (probability) density, distribution or quantile functions, we provide MPFR versions.
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) pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)
x,q, lambda, size,prob, mu, mean,sd, shape,rate,scale |
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log, log.p, lower.tail |
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useLog |
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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).
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.
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.
x <- 1400+ 0:10
print(dpois(x, 1000), digits =18) ## standard R's double precision
dpois(mpfr(x, 120), 1000)## more accuracy for the same
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
.mpfr_erange_set(value = (1-2^-52)*.mpfr_erange(c("min.emin","max.emax")))
tens <- mpfr(10^(4:7), 128)
pnorm(tens, lower.tail=FALSE, log.p=TRUE) # "works"
## reset to previous
.mpfr_erange_set( , old_eranges)
pnorm(tens, lower.tail=FALSE, log.p=TRUE) # all but first underflow to -InfPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.