# distr-etc: Distribution Functions etc (MPFR) In Rmpfr: R MPFR - Multiple Precision Floating-Point Reliable

## Description

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

## Usage

 ```1 2 3 4 5``` ```dpois (x, lambda, log = FALSE) dbinom(x, size, prob, log = FALSE) dnorm (x, mean = 0, sd = 1, log = FALSE) pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) ```

## Arguments

 `x,q, lambda, size,prob, mean,sd` `numeric` or `mpfr` vectors. All of these are “recycled” to the length of the longest one.
 `log, log.p, lower.tail` logical, see `pnorm`, `dpois`, etc.

## 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.

`pnorm`, `dbinom`, `dpois` in standard package stats.
`pbetaI(x, a,b)` is a `mpfr` version of `pbeta` only for integer `a` and `b`.
 ``` 1 2 3 4 5 6 7 8 9 10``` ```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 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)) ```