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DPQ (version 0.6-2)

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. -- 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

2,201

Version

0.6-2

License

GPL (>= 2) | file LICENSE

Homepage

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

Maintainer

Martin Maechler

Last Published

September 6th, 2026

Functions in DPQ (0.6-2)

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

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

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

Psi Gamma Functions Workhorse from R's API

Asymptotic Noncentral t Distribution Density by Viechtbauer

TOMS 1006 - Fast and Accurate Generalized Incomplete Gamma Function

Gamma Density Function Alternatives

Distribution Utilities "dpq"

Non-central t-Distribution Density - Algorithms and Approximations

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

Base-2 Representation and Multiplication of Numbers

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

(Log) Beta and Ratio of Gammas Approximations

Accurate Approximation of log(a * beta(a,b)) for small a

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

Transform Hypergeometric Distribution Parameters to Binomial Probability

Accurate log(gamma(a+1))

R versions of Simple Formulas for Logarithmic Binomial Coefficients

Properly Compute the Logarithm of a Sum (of Exponentials)

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

Asymptotic Log Gamma Function

Gamma Function Versions

Simple R level Newton Algorithm, Mostly for Didactical Reasons

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

Compute Logarithm of a Sum with Signed Large Summands

Accurate log(1+x) - x Computation

Logspace Arithmetix -- Addition and Subtraction

Continued Fraction Approximation of Log-Related Power Series

Numerical Utilities - Functions, Constants

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

HyperGeometric Distribution via Approximate Binomial Distribution

Compute Hypergeometric Probabilities via Binomial Approximations

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

Peizer's Normal Approximation to the Cumulative Hyperbolic

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

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

Molenaar's Normal Approximations to the Hypergeometric Distribution

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

Pure R Implementation of Old pbeta()

pnchisqWienergerm

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

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

Noncentral Beta Probabilities

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

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

Non-central t Probability Distribution - Algorithms and Approximations

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

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

Plot 2 Noncentral Distribution Curves for Visual Comparison

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

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

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

pt_Witkovsky_Tab1

Viktor Witosky's Table_1 pt() Examples

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute (Approximate) Quantiles of the Gamma Distribution

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

Compute (Approximate) Quantiles of the Beta Distribution

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

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

Asymptotic Approximation to Outer Tail of qnorm()

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

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

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

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

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

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

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

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

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

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

Chebyshev Polynomial Evaluation

Bernoulli Numbers

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

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

pbeta() 'bpser' series computation

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

tools:::Rd_package_title("DPQ")

Normalized Incomplete Beta Function "Like" pbeta()

Approximations of the (Noncentral) Chi-Squared Density

Binomial Deviance -- Auxiliary Functions for dgamma() Etc