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DPQ (version 0.5-8)

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

593

Version

0.5-8

License

GPL (>= 2)

Homepage

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

Maintainer

Martin Maechler

Last Published

December 1st, 2023

Functions in DPQ (0.5-8)

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

Utility Functions for dgamma() -- Pure R Versions

Chebyshev Polynomial Evaluation

Distribution Utilities "dpq"

Non-central t-Distribution Density - Algorithms and Approximations

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

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

Gamma Density Function Alternatives

Psi Gamma Functions Workhorse from R's API

Noncentral t Distribution Density by Viechtbauer

Compute Logarithm of a Sum with Signed Large Summands

Continued Fraction Approximation of Log-Related Power Series

Logspace Arithmetix -- Addition and Subtraction

Gamma Function Versions

Properly Compute the Logarithm of a Sum (of Exponentials)

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

Base-2 Representation and Multiplication of Numbers

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Compute Hypergeometric Probabilities via Binomial Approximations

Transform Hypergeometric Distribution Parameters to Binomial Probability

R versions of Simple Formulas for Logarithmic Binomial Coefficients

(Log) Beta Approximations

Accurate log(gamma(a+1))

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

HyperGeometric Distribution via Approximate Binomial Distribution

Simple R level Newton Algorithm, Mostly for Didactical Reasons

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

Asymptotic Log Gamma Function

Molenaar's Normal Approximations to the Hypergeometric Distribution

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

Numerical Utilities - Functions, Constants

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

Plot 2 Noncentral Distribution Curves for Visual Comparison

Accurate log(1+x) - x Computation

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

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

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

Noncentral Beta Probabilities

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

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

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute (Approximate) Quantiles of the Gamma Distribution

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

Non-central t Probability Distribution - Algorithms and Approximations

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

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

Peizer's Normal Approximation to the Cumulative Hyperbolic

Pure R Implementation of Old pbeta()

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

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

pnchisqWienergerm

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

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

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

Direct Computation of 'ppois()' Poisson Distribution Probabilities

Compute (Approximate) Quantiles of the Beta Distribution

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

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

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

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

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

Asymptotic Approximation to Outer Tail of qnorm()

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

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

pbeta() 'bpser' series computation

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

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

Bernoulli Numbers

tools:::Rd_package_title("DPQ")

Approximations of the (Noncentral) Chi-Squared Density