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DPQ (version 0.4-1)

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

0.4-1

License

GPL (>= 2)

Maintainer

Martin Maechler

Last Published

June 19th, 2020

Functions in DPQ (0.4-1)

Utility Functions for dgamma() -- Pure R Versions

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

Gamma Density Function Alternatives

Non-central t-Distribution Density - Algorithms and Approximations

Approximations of the (Noncentral) Chi-Squared Density

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

Bernoulli Numbers

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

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

Noncentral t Distribution Density by W.V.

Accurate log(1+x) - x

HyperGeometric Distribution via Approximate Binomial Distribution

Transform Hypergeometric Distribution Parameters to Binomial Probability

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Pure R Implementation of Old pbeta()

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

Compute Hypergeometric Probabilities via Binomial Approximations

Asymptotic Log Gamma Function

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Logspace Arithmetix -- Addition and Subtraction

Continued Fraction Approximation of Log-Related Series

Accurate log(gamma(a+1))

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

R-only version of R's original phyper() algorithm

Compute (Approximate) Quantiles of the Gamma Distribution

Pure R version of R's C level phyper()

R versions of Simple Formulas for Logarithmic Binomial Coefficients

Compute (Approximate) Quantiles of the Beta Distribution

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

(Log) Beta Approximations

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

Properly Compute the Logarithm of a Sum (of Exponentials)

Noncentral Beta Probabilities

Compute Logarithm of a Sum with Signed Large Summands

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

Peizer's Normal Approximation to the Cumulative Hyperbolic

Molenaar's Normal Approximations to the Hypergeometric Distribution

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

Compute Approximate Quantiles of Non-Central t Distribution

Compute Approximate Quantiles of the Chi-Squared Distribution

Numerical Utilities - Functions, Constants

The Four (4) Symmetric phyper() calls.

pnchisqWienergerm

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

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

Plot 2 Noncentral Distribution Curves for Visual Comparison

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Non-central t Probability Distribution - Algorithms and Approximations