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DPQ (version 0.6-0)

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

599

Version

0.6-0

License

GPL (>= 2) | file LICENSE

Homepage

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

Maintainer

Martin Maechler

Last Published

July 8th, 2025

Functions in DPQ (0.6-0)

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

TOMS 1006 - Fast and Accurate Generalized Incomplete Gamma Function

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

Psi Gamma Functions Workhorse from R's API

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

Asymptotic Noncentral t Distribution Density by Viechtbauer

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

Non-central t-Distribution Density - Algorithms and Approximations

Gamma Density Function Alternatives

Distribution Utilities "dpq"

Base-2 Representation and Multiplication of Numbers

(Log) Beta and Ratio of Gammas Approximations

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

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

Gamma Function Versions

Asymptotic Log Gamma Function

R versions of Simple Formulas for Logarithmic Binomial Coefficients

Transform Hypergeometric Distribution Parameters to Binomial Probability

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

Accurate log(gamma(a+1))

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

Numerical Utilities - Functions, Constants

Continued Fraction Approximation of Log-Related Power Series

Logspace Arithmetix -- Addition and Subtraction

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

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Pure R Implementation of Old pbeta()

Compute Logarithm of a Sum with Signed Large Summands

Molenaar's Normal Approximations to the Hypergeometric Distribution

Properly Compute the Logarithm of a Sum (of Exponentials)

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

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

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

HyperGeometric Distribution via Approximate Binomial Distribution

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

Peizer's Normal Approximation to the Cumulative Hyperbolic

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

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Accurate log(1+x) - x Computation

Compute Hypergeometric Probabilities via Binomial Approximations

Non-central t Probability Distribution - Algorithms and Approximations

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

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

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

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

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

pnchisqWienergerm

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

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

Plot 2 Noncentral Distribution Curves for Visual Comparison

Noncentral Beta Probabilities

pt_Witkovsky_Tab1

Viktor Witosky's Table_1 pt() Examples

Compute Approximate Quantiles of the Chi-Squared Distribution

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

Direct Computation of 'ppois()' Poisson Distribution Probabilities

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

Compute (Approximate) Quantiles of the Beta Distribution

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

Asymptotic Approximation to Outer Tail of qnorm()

Compute (Approximate) Quantiles of the Gamma Distribution

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

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

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

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

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

Bernoulli Numbers

tools:::Rd_package_title("DPQ")

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

Chebyshev Polynomial Evaluation

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

Normalized Incomplete Beta Function "Like" pbeta()

Approximations of the (Noncentral) Chi-Squared Density

Binomial Deviance -- Auxiliary Functions for dgamma() Etc

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

pbeta() 'bpser' series computation