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DPQ (version 0.6-1)

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. -- For several distribution functions, provide functions implementing formulas from Johnson, Kotz, and Kemp (1992) and Johnson, Kotz, and Balakrishnan (1995) for discrete or continuous distributions respectively. 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

6,713

Version

0.6-1

License

GPL (>= 2) | file LICENSE

Homepage

https://specfun.r-forge.r-project.org/

Maintainer

Martin Maechler

Last Published

October 13th, 2025

Functions in DPQ (0.6-1)

Psi Gamma Functions Workhorse from R's API

Gamma Density Function Alternatives

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

TOMS 1006 - Fast and Accurate Generalized Incomplete Gamma Function

Distribution Utilities "dpq"

Accurate exp(x) - 1 - x (for smallish |x|)

Non-central t-Distribution Density - Algorithms and Approximations

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

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

Asymptotic Noncentral t Distribution Density by Viechtbauer

Compute log( Gamma(x+1) ) Accurately in [-0.2, 1.25]

(Log) Beta and Ratio of Gammas Approximations

Gamma Function Versions

R versions of Simple Formulas for Logarithmic Binomial Coefficients

Base-2 Representation and Multiplication of Numbers

Compute 1/Gamma(x+1) - 1 Accurately

Accurate log(gamma(a+1))

Transform Hypergeometric Distribution Parameters to Binomial Probability

Log Gamma(p) for Positive p by Pugh's Method (11 Terms)

Asymptotic Log Gamma Function

Compute Logarithm of a Sum with Signed Large Summands

Logspace Arithmetix -- Addition and Subtraction

Accurate log(1+x) - x Computation

Continued Fraction Approximation of Log-Related Power Series

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

pbeta() Approximations of Abramowitz & Stegun, \(26.5.\{20,21\}\)

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

Numerical Utilities - Functions, Constants

Simple R level Newton Algorithm, Mostly for Didactical Reasons

HyperGeometric Distribution via Approximate Binomial Distribution

Properly Compute the Logarithm of a Sum (of Exponentials)

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

Pure R Implementation of Old pbeta()

Compute Hypergeometric Probabilities via Binomial Approximations

Peizer's Normal Approximation to the Cumulative Hyperbolic

Molenaar's Normal Approximations to the Hypergeometric Distribution

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

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

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

The Four (4) Symmetric 'phyper()' Calls

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

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

Noncentral Beta Probabilities

Non-central t Probability Distribution - Algorithms and Approximations

Plot 2 Noncentral Distribution Curves for Visual Comparison

X to Power of Y -- R C API R_pow()

pnchisqWienergerm

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

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

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

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

Asymptotic Approximation to Outer Tail of qnorm()

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute (Approximate) Quantiles of the Gamma Distribution

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

Accurate \((1+x)^y\), notably for small \(|x|\)

Direct Computation of 'ppois()' Poisson Distribution Probabilities

pt_Witkovsky_Tab1

Viktor Witosky's Table_1 pt() Examples

Compute (Approximate) Quantiles of the Beta Distribution

Compute Approximate Quantiles of the (Non-Central) t-Distribution

Pure R Implementation of R's qt() / qnt()

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

Pure R Implementation of R's C-level t-Distribution Quantiles qt()

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

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

TOMS 708 Approximation REXP(x) of expm1(x) = exp(x) - 1

Stirling's Error Function - Auxiliary for Gamma, Beta, etc

'uniroot()'-based Computing of t-Distribution Quantiles

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

Bernoulli Numbers

Chebyshev Polynomial Evaluation

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

Binomial Deviance -- Auxiliary Functions for dgamma() Etc

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

Normalized Incomplete Beta Function "Like" pbeta()

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

pbeta() 'bpser' series computation

Approximations of the (Noncentral) Chi-Squared Density

tools:::Rd_package_title("DPQ")