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DPQ (version 0.5-3)

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

583

Version

0.5-3

License

GPL (>= 2)

Homepage

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

Maintainer

Martin Maechler

Last Published

December 1st, 2022

Functions in DPQ (0.5-3)

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

tools:::Rd_package_title("DPQ")

Bernoulli Numbers

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

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

Approximations of the (Noncentral) Chi-Squared Density

Gamma Density Function Alternatives

Chebyshev Polynomial Evaluation

pbeta() 'bpser' series computation

Utility Functions for dgamma() -- Pure R Versions

Base-2 Representation and Multiplication of Numbers

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

Psi Gamma Functions Workhorse from R's API

Gamma Function Versions

Transform Hypergeometric Distribution Parameters to Binomial Probability

(Log) Beta Approximations

Noncentral t Distribution Density by W.V.

Non-central t-Distribution Density - Algorithms and Approximations

dhyperBinMolenaar

HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation

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

Logspace Arithmetix -- Addition and Subtraction

Properly Compute the Logarithm of a Sum (of Exponentials)

Accurate log(1+x) - x Computation

Compute Logarithm of a Sum with Signed Large Summands

R versions of Simple Formulas for Logarithmic Binomial Coefficients

Continued Fraction Approximation of Log-Related Power Series

Simple R level Newton Algorithm, Mostly for Didactical Reasons

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

Accurate log(gamma(a+1))

Asymptotic Log Gamma Function

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

Pearson's incomplete Beta Approximation to the Hyperbolic Distribution

Peizer's Normal Approximation to the Cumulative Hyperbolic

Molenaar's Normal Approximations to the Hypergeometric Distribution

phyperBinMolenaar

HyperGeometric Distribution via Molenaar's Binomial Approximation

Numerical Utilities - Functions, Constants

Compute Hypergeometric Probabilities via Binomial Approximations

phyperApprAS152

Normal Approximation to cumulative Hyperbolic Distribution -- AS 152

Pure R Implementation of Old pbeta()

HyperGeometric Distribution via Approximate Binomial Distribution

pnchisqWienergerm

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

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

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

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

Noncentral Beta Probabilities

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

The Four (4) Symmetric phyper() calls.

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

Plot 2 Noncentral Distribution Curves for Visual Comparison

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

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

Compute Approximate Quantiles of the Chi-Squared Distribution

Compute (Approximate) Quantiles of the Gamma Distribution

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

Compute (Approximate) Quantiles of the Beta Distribution

Non-central t Probability Distribution - Algorithms and Approximations

Compute Approximate Quantiles of Noncentral Chi-Squared Distribution

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

Asymptotic Approximation to Outer Tail of qnorm()

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

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

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

Direct Computation of 'ppois()' Poisson Distribution Probabilities

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

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

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

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