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DPQ (version 0.3-5)

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

599

Version

0.3-5

License

GPL (>= 2)

Maintainer

Martin Maechler

Last Published

October 21st, 2019

Functions in DPQ (0.3-5)

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

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Compute (Approximate) Quantiles of the Beta Distribution

Properly Compute the Logarithm of a Sum

Approximations of the (Noncentral) Chi-Squared Density

(Log) Beta Approximations

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

Accurate log(gamma(a+1))

Plot 2 Noncentral Distribution Curves for Visual Comparison

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

Noncentral Beta Probabilities

(Probabilities of Non-Central Chi-squared Distribution for Special Cases

(Approximate) Probabilities of Non-Central Chi-squared Distribution

Compute Approximate Quantiles of Non-Central t Distribution

Gamma Density Function Alternatives

Continued Fraction Approximation of Log-Related Series

Utility Functions for dgamma() -- Pure R Versions

Accurate log(1+x) - x

Numerical Utilities - Functions, Constants

Pure R Implementation of Old pbeta()

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

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

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute (Approximate) Quantiles of the Gamma Distribution

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

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

Non-central t-Distribution Density - Algorithms and Approximations

pnchisqWienergerm

Wienergerm Approximations to (Non-Central) Chi-squared Probabilities

Non-central t Probability Distribution - Algorithms and Approximations

Compute Logarithm of a Sum with Signed Large Summands

Logspace Arithmetix -- Addition and Subtraction

Noncentral t Distribution Density by W.V.