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DPQ (version 0.3-3)

Density, Probability, Quantile ('DPQ') Computations

Description

Computations for approximations and alternatives for the 'DPQ' (Density (pdf), Probability (cdf) and Quantile) functions for probability distributions in R. Primary focus is on (central and non-central) beta, gamma and related distributions such as the chi-squared, F, and t. -- This is for the use of researchers in these numerical approximation implementations, notably for my own use in order to improve R`s own pbeta(), qgamma(), ..., etc: {'"dpq"'-functions}. -- We plan to complement with 'DPQmpfr' to be suggested later.

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Version

Install

install.packages('DPQ')

Monthly Downloads

593

Version

0.3-3

License

GPL (>= 2)

Maintainer

Martin Maechler

Last Published

October 2nd, 2019

Functions in DPQ (0.3-3)

Gamma Density Function Alternatives

Noncentral t Distribution Density by W.V.

Approximations of the (Noncentral) Chisquared Density

(Log) Beta Approximations

Format Numbers in [0,1] with "Precise" Result

Compute \(E[\chi_\nu] / \sqrt{\nu}\) useful for t- and chi-Distributions

Utility Functions for dgamma() -- Pure R Versions

Non-central t-Distribution Density - Algorithms and Approximations

Compute log(gamma(b)/gamma(a+b)) when b >= 8

Numerical Utilities - Functions, Constants

Compute Logarithm of a Sum with Signed Large Summands

Compute (Approximate) Quantiles of the Beta Distribution

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Logspace Arithmetix -- Addition and Subtraction

(Probabilities of Non-Central Chisquared Distribution for Special Cases

Pure R Implementation of Old pbeta()

(Approximate) Probabilities of Non-Central Chisquared Distribution

Compute f(a) = \(\mathrm{log}\)(1 - \(\mathrm{exp}\)(-a)) Numerically Optimally

Accurate log(gamma(a+1))

Plot 2 Noncentral Distribution Curves for Visual Comparison

Accurate log(1+x) - x

Noncentral Beta Probabilities

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

Approximations to 'qnorm()', i.e., \(z_\alpha\)

Non-central t Probability Distribution - Algorithms and Approximations

Compute Relative Size of i-th term of Poisson Distribution Series

Compute Approximate Quantiles of Non-Central t Distribution

pnchisqWienergerm

Wienergerm Approximations to (Non-Central) Chisquare Probabilities

Continued Fraction Approximation of Log-Related Series

Properly Compute the Logarithm of a Sum

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute (Approximate) Quantiles of the Gamma Distribution