HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation
Compute log(gamma(b)/gamma(a+b)) when b >= 8
Utility Functions for dgamma()
-- Pure R Versions
Non-central t-Distribution Density - Algorithms and Approximations
DPQ
Bernoulli Numbers
Compute \(E[\chi_\nu] / \sqrt{\nu}\)
useful for t- and chi-Distributions
Noncentral t Distribution Density by W.V.
Approximations of the (Noncentral) Chi-Squared Density
Gamma Density Function Alternatives
R versions of Simple Formulas for Logarithmic Binomial Coefficients
(Log) Beta Approximations
Continued Fraction Approximation of Log-Related Series
Accurate log(gamma(a+1))
Logspace Arithmetix -- Addition and Subtraction
Pearson's incomplete Beta Approximation to the Hyperbolic Distribution
HyperGeometric Distribution via Molenaar's Binomial Approximation
Compute Logarithm of a Sum with Signed Large Summands
Compute f(a) = \(\mathrm{log}\)(1 - \(\mathrm{exp}\)(-a))
Numerically Optimally
Molenaar's Normal Approximations to the Hypergeometric Distribution
Format Numbers in [0,1] with "Precise" Result
Transform Hypergeometric Distribution Parameters to Binomial Probability
Properly Compute the Logarithm of a Sum (of Exponentials)
Peizer's Normal Approximation to the Cumulative Hyperbolic
Accurate log(1+x) - x
Pure R Implementation of Old pbeta()
The Four (4) Symmetric phyper() calls.
Compute Hypergeometric Probabilities via Binomial Approximations
HyperGeometric Distribution via Approximate Binomial Distribution
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution
Normal Approximation to cumulative Hyperbolic Distribution -- AS 152
Simple R level Newton Algorithm, Mostly for Didactical Reasons
Asymptotic Log Gamma Function
Numerical Utilities - Functions, Constants
Noncentral Beta Probabilities
R -only version of R 's original phyper() algorithm
Pure R version of R's C level phyper()
Wienergerm Approximations to (Non-Central) Chi-squared Probabilities
Plot 2 Noncentral Distribution Curves for Visual Comparison
Approximations to 'qnorm()', i.e., \(z_\alpha\)
Compute Approximate Quantiles of the Chi-Squared Distribution
(Approximate) Probabilities of Non-Central Chi-squared Distribution
Pure R version of R 's qnorm()
with Diagnostics and Tuning Parameters
Compute (Approximate) Quantiles of the Gamma Distribution
Compute Approximate Quantiles of Non-Central t Distribution
Bounds for 1-Phi(.) -- Mill's Ratio related Bounds for pnorm()
Direct Computation of 'ppois()' Poisson Distribution Probabilities
Compute (Approximate) Quantiles of the Beta Distribution
Compute Relative Size of i-th term of Poisson Distribution Series
(Probabilities of Non-Central Chi-squared Distribution for Special Cases
Non-central t Probability Distribution - Algorithms and Approximations