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DPQ (version 0.4-2)

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

0.4-2

License

GPL (>= 2)

Maintainer

Martin Maechler

Last Published

November 9th, 2020

Functions in DPQ (0.4-2)

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

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

Utility Functions for dgamma() -- Pure R Versions

Non-central t-Distribution Density - Algorithms and Approximations

Bernoulli Numbers

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

Noncentral t Distribution Density by W.V.

Approximations of the (Noncentral) Chi-Squared Density

Gamma Density Function Alternatives

R versions of Simple Formulas for Logarithmic Binomial Coefficients

(Log) Beta Approximations

Continued Fraction Approximation of Log-Related Series

Accurate log(gamma(a+1))

Logspace Arithmetix -- Addition and Subtraction

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

Compute Logarithm of a Sum with Signed Large Summands

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

Molenaar's Normal Approximations to the Hypergeometric Distribution

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

Transform Hypergeometric Distribution Parameters to Binomial Probability

Properly Compute the Logarithm of a Sum (of Exponentials)

Peizer's Normal Approximation to the Cumulative Hyperbolic

Accurate log(1+x) - x

Pure R Implementation of Old pbeta()

The Four (4) Symmetric phyper() calls.

Compute Hypergeometric Probabilities via Binomial Approximations

HyperGeometric Distribution via Approximate Binomial Distribution

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Asymptotic Log Gamma Function

Numerical Utilities - Functions, Constants

Noncentral Beta Probabilities

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

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

pnchisqWienergerm

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

Plot 2 Noncentral Distribution Curves for Visual Comparison

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

Compute Approximate Quantiles of the Chi-Squared Distribution

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

Pure R version of R's qnorm() with Diagnostics and Tuning Parameters

Compute (Approximate) Quantiles of the Gamma Distribution

Compute Approximate Quantiles of Non-Central t Distribution

Bounds for 1-Phi(.) -- Mill's Ratio related Bounds for pnorm()

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Compute (Approximate) Quantiles of the Beta Distribution

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

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

Non-central t Probability Distribution - Algorithms and Approximations