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
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
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
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
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