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DPQ (version 0.4-3)

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 standard R pbeta(), qgamma(), ..., etc: {'"dpq"'-functions}.

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Version

Install

install.packages('DPQ')

Monthly Downloads

593

Version

0.4-3

License

GPL (>= 2)

Maintainer

Martin Maechler

Last Published

May 5th, 2021

Functions in DPQ (0.4-3)

R's C (Mathlib) dbinom_raw() Binomial Probability pure R Function

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

(Log) Beta Approximations

Approximations of the (Noncentral) Chi-Squared Density

Utility Functions for dgamma() -- Pure R Versions

Pure R Versions of R's C (Mathlib) dnbinom() Negative Binomial Probabilities

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

Transform Hypergeometric Distribution Parameters to Binomial Probability

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

Bernoulli Numbers

Accurate log(gamma(a+1))

Gamma Density Function Alternatives

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

Non-central t-Distribution Density - Algorithms and Approximations

Asymptotic Log Gamma Function

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Peizer's Normal Approximation to the Cumulative Hyperbolic

Compute Hypergeometric Probabilities via Binomial Approximations

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

Pure R Implementation of Old pbeta()

Numerically Stable p1l1(t) = (t+1)*log(1+t) - t

The Four (4) Symmetric phyper() calls.

Logspace Arithmetix -- Addition and Subtraction

Continued Fraction Approximation of Log-Related Power Series

R versions of Simple Formulas for Logarithmic Binomial Coefficients

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

Pure R Implementation of R's qbinom() with Tuning Parameters

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute \(\mathrm{log}\)(1 - \(\mathrm{exp}\)(-a)) and \(\log(1 + \exp(x))\) Numerically Optimally

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Accurate log(1+x) - x

Properly Compute the Logarithm of a Sum (of Exponentials)

Plot 2 Noncentral Distribution Curves for Visual Comparison

Compute Logarithm of a Sum with Signed Large Summands

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

Noncentral Beta Probabilities

Compute (Approximate) Quantiles of the Beta Distribution

Numerical Utilities - Functions, Constants

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Non-central t Probability Distribution - Algorithms and Approximations

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

Pure R Implementation of R's qpois() with Tuning Parameters

Noncentral t Distribution Density by W.V.

HyperGeometric Distribution via Approximate Binomial Distribution

Asymptotic Approxmation of (Extreme Tail) 'pnorm()'

Molenaar's Normal Approximations to the Hypergeometric Distribution

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

pnchisqWienergerm

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

Compute Approximate Quantiles of Non-Central t Distribution

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

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

Compute (Approximate) Quantiles of the Gamma Distribution

Pure R Implementation of R's qnbinom() with Tuning Parameters

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

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

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution