| dbinom_raw |
R's C Mathlib (Rmath) dbinom_raw() Binomial Probability pure R Function |
| dchisqAsym |
Approximations of the (Noncentral) Chi-Squared Density |
| dgamma.R |
Gamma Density Function Alternatives |
| dhyperBinMolenaar |
HyperGeometric (Point) Probabilities via Molenaar's Binomial Approximation |
| dnbinom.mu |
Pure R Versions of R's C (Mathlib) dnbinom() Negative Binomial Probabilities |
| dnbinomR |
Pure R Versions of R's C (Mathlib) dnbinom() Negative Binomial Probabilities |
| dnchisqBessel |
Approximations of the (Noncentral) Chi-Squared Density |
| dnchisqR |
Approximations of the (Noncentral) Chi-Squared Density |
| dnoncentchisq |
Approximations of the (Noncentral) Chi-Squared Density |
| dntJKBf |
Non-central t-Distribution Density - Algorithms and Approximations |
| dntJKBf1 |
Non-central t-Distribution Density - Algorithms and Approximations |
| dpois_raw |
Binomial Deviance - Auxiliary Functions for 'dgamma()' Etc |
| dpois_simpl |
Binomial Deviance - Auxiliary Functions for 'dgamma()' Etc |
| dpois_simpl0 |
Binomial Deviance - Auxiliary Functions for 'dgamma()' Etc |
| DPQ |
Density, Probability, Quantile ('DPQ') Computations |
| dpsifn |
Psi Gamma Functions Workhorse from R's API |
| dtWV |
Asymptotic Noncentral t Distribution Density by Viechtbauer |
| lbetaI |
(Log) Beta and Ratio of Gammas Approximations |
| lbetaM |
(Log) Beta and Ratio of Gammas Approximations |
| lbetaMM |
(Log) Beta and Ratio of Gammas Approximations |
| lbeta_asy |
(Log) Beta and Ratio of Gammas Approximations |
| lb_chi0 |
Compute E[chi_nu]/sqrt(nu) useful for t- and chi-Distributions |
| lb_chi00 |
Compute E[chi_nu]/sqrt(nu) useful for t- and chi-Distributions |
| lb_chiAsymp |
Compute E[chi_nu]/sqrt(nu) useful for t- and chi-Distributions |
| ldexp |
Base-2 Representation and Multiplication of Numbers |
| lfastchoose |
R versions of Simple Formulas for Logarithmic Binomial Coefficients |
| lgamma1p |
Accurate 'log(gamma(a+1))' |
| lgamma1p. |
Accurate 'log(gamma(a+1))' |
| lgamma1pC |
Accurate 'log(gamma(a+1))' |
| lgamma1p_series |
Accurate 'log(gamma(a+1))' |
| lgammaAsymp |
Asymptotic Log Gamma Function |
| lgammacor |
Stirling's Error Function - Auxiliary for Gamma, Beta, etc |
| log1mexp |
Compute log(1 - exp(-a)) and log(1 + exp(x)) Numerically Optimally |
| log1mexpC |
Compute log(1 - exp(-a)) and log(1 + exp(x)) Numerically Optimally |
| log1pexpC |
Compute log(1 - exp(-a)) and log(1 + exp(x)) Numerically Optimally |
| log1pmx |
Accurate 'log(1+x) - x' Computation |
| log1pmxC |
Accurate 'log(1+x) - x' Computation |
| logcf |
Continued Fraction Approximation of Log-Related Power Series |
| logcfR |
Continued Fraction Approximation of Log-Related Power Series |
| logcfR. |
Continued Fraction Approximation of Log-Related Power Series |
| logQab_asy |
(Log) Beta and Ratio of Gammas Approximations |
| logr |
Numerical Utilities - Functions, Constants |
| logspace.add |
Logspace Arithmetix - Addition and Subtraction |
| logspace.sub |
Logspace Arithmetix - Addition and Subtraction |
| lssum |
Compute Logarithm of a Sum with Signed Large Summands |
| lsum |
Properly Compute the Logarithm of a Sum (of Exponentials) |
| p1l1 |
Numerically Stable p1l1(t) = (t+1)*log(1+t) - t |
| p1l1. |
Numerically Stable p1l1(t) = (t+1)*log(1+t) - t |
| p1l1p |
Numerically Stable p1l1(t) = (t+1)*log(1+t) - t |
| p1l1ser |
Numerically Stable p1l1(t) = (t+1)*log(1+t) - t |
| pbetaRv1 |
Pure R Implementation of Old pbeta() |
| pchisqV |
Wienergerm Approximations to (Non-Central) Chi-squared Probabilities |
| pchisqW |
Wienergerm Approximations to (Non-Central) Chi-squared Probabilities |
| pchisqW. |
Wienergerm Approximations to (Non-Central) Chi-squared Probabilities |
| pchisqW.R |
Wienergerm Approximations to (Non-Central) Chi-squared Probabilities |
| pdhyper |
Pure R version of R's C level phyper() |
| phyper1molenaar |
Molenaar's Normal Approximations to the Hypergeometric Distribution |
| phyper2molenaar |
Molenaar's Normal Approximations to the Hypergeometric Distribution |
| phyperAllBin |
Compute Hypergeometric Probabilities via Binomial Approximations |
| phyperAllBinM |
Compute Hypergeometric Probabilities via Binomial Approximations |
| phyperApprAS152 |
Normal Approximation to cumulative Hyperbolic Distribution - AS 152 |
| phyperBin.1 |
HyperGeometric Distribution via Approximate Binomial Distribution |
| phyperBin.2 |
HyperGeometric Distribution via Approximate Binomial Distribution |
| phyperBin.3 |
HyperGeometric Distribution via Approximate Binomial Distribution |
| phyperBin.4 |
HyperGeometric Distribution via Approximate Binomial Distribution |
| phyperBinMolenaar |
HyperGeometric Distribution via Molenaar's Binomial Approximation |
| phyperBinMolenaar.1 |
HyperGeometric Distribution via Molenaar's Binomial Approximation |
| phyperBinMolenaar.2 |
HyperGeometric Distribution via Molenaar's Binomial Approximation |
| phyperBinMolenaar.3 |
HyperGeometric Distribution via Molenaar's Binomial Approximation |
| phyperBinMolenaar.4 |
HyperGeometric Distribution via Molenaar's Binomial Approximation |
| phyperIbeta |
Pearson's incomplete Beta Approximation to the Hyperbolic Distribution |
| phyperPeizer |
Peizer's Normal Approximation to the Cumulative Hyperbolic |
| phyperR |
R-only version of R's original phyper() algorithm |
| phyperR2 |
Pure R version of R's C level phyper() |
| phypers |
The Four (4) Symmetric 'phyper()' Calls |
| pl2curves |
Plot 2 Noncentral Distribution Curves for Visual Comparison |
| plRpois |
Compute Relative Size of i-th term of Poisson Distribution Series |
| pnbetaAppr2 |
Noncentral Beta Probabilities |
| pnbetaAppr2v1 |
Noncentral Beta Probabilities |
| pnbetaAS310 |
Noncentral Beta Probabilities |
| pnchi1sq |
(Probabilities of Non-Central Chi-squared Distribution for Special Cases |
| pnchi3sq |
(Probabilities of Non-Central Chi-squared Distribution for Special Cases |
| pnchisq |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqAbdelAty |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqBolKuz |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqIT |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqPatnaik |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqPearson |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqRC |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqSankaran_d |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqT93 |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqT93.a |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqT93.b |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqTerms |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisqV |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnchisq_ss |
(Approximate) Probabilities of Non-Central Chi-squared Distribution |
| pnormAsymp |
Asymptotic Approxmation of (Extreme Tail) 'pnorm()' |
| pnormL_LD10 |
Bounds for 1-Phi(.) - Mill's Ratio related Bounds for pnorm() |
| pnormU_S53 |
Bounds for 1-Phi(.) - Mill's Ratio related Bounds for pnorm() |
| pnt3150 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pnt3150.1 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntChShP94 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntChShP94.1 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntGST23_1 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntGST23_T6 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntGST23_T6.1 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntJW39 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntJW39.0 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntLrg |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntP94 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntP94.1 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntR |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntR1 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pntVW13 |
Non-central t Probability Distribution - Algorithms and Approximations |
| pow |
X to Power of Y - R C API 'R_pow()' |
| pow1p |
Accurate (1+x)^y, notably for small |x| |
| pow_di |
X to Power of Y - R C API 'R_pow()' |
| ppoisD |
Direct Computation of 'ppois()' Poisson Distribution Probabilities |
| ppoisErr |
Direct Computation of 'ppois()' Poisson Distribution Probabilities |
| pt_Witkovsky_Tab1 |
Viktor Witosky's Table_1 pt() Examples |
| Qab_terms |
(Log) Beta and Ratio of Gammas Approximations |
| qbeta.R |
Compute (Approximate) Quantiles of the Beta Distribution |
| qbetaAppr |
Compute (Approximate) Quantiles of the Beta Distribution |
| qbetaAppr.1 |
Compute (Approximate) Quantiles of the Beta Distribution |
| qbetaAppr.2 |
Compute (Approximate) Quantiles of the Beta Distribution |
| qbetaAppr.3 |
Compute (Approximate) Quantiles of the Beta Distribution |
| qbetaAppr.4 |
Compute (Approximate) Quantiles of the Beta Distribution |
| qbinomR |
Pure R Implementation of R's qbinom() with Tuning Parameters |
| qchisqAppr |
Compute Approximate Quantiles of the Chi-Squared Distribution |
| qchisqAppr.0 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqAppr.1 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqAppr.2 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqAppr.3 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqAppr.R |
Compute Approximate Quantiles of the Chi-Squared Distribution |
| qchisqApprCF1 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqApprCF2 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqCappr.2 |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqKG |
Compute Approximate Quantiles of the Chi-Squared Distribution |
| qchisqN |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qchisqWH |
Compute Approximate Quantiles of the Chi-Squared Distribution |
| qgamma.R |
Compute (Approximate) Quantiles of the Gamma Distribution |
| qgammaAppr |
Compute (Approximate) Quantiles of the Gamma Distribution |
| qgammaApprKG |
Compute (Approximate) Quantiles of the Gamma Distribution |
| qgammaApprSmallP |
Compute (Approximate) Quantiles of the Gamma Distribution |
| qnbinomR |
Pure R Implementation of R's qnbinom() with Tuning Parameters |
| qnchisqAbdelAty |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qnchisqAppr |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qnchisqBolKuz |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qnchisqPatnaik |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qnchisqPearson |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qnchisqSankaran_d |
Compute Approximate Quantiles of Noncentral Chi-Squared Distribution |
| qnormAppr |
Approximations to 'qnorm()', i.e., z_alpha |
| qnormAsymp |
Asymptotic Approximation to Outer Tail of qnorm() |
| qnormCappr |
Approximations to 'qnorm()', i.e., z_alpha |
| qnormR |
Pure R version of R's 'qnorm()' with Diagnostics and Tuning Parameters |
| qnormR1 |
Pure R version of R's 'qnorm()' with Diagnostics and Tuning Parameters |
| qnormUappr |
Approximations to 'qnorm()', i.e., z_alpha |
| qnormUappr6 |
Approximations to 'qnorm()', i.e., z_alpha |
| qntR |
Pure R Implementation of R's qt() / qnt() |
| qntR1 |
Pure R Implementation of R's qt() / qnt() |
| qpoisR |
Pure R Implementation of R's qpois() with Tuning Parameters |
| qs |
Wienergerm Approximations to (Non-Central) Chi-squared Probabilities |
| qtAppr |
Compute Approximate Quantiles of the (Non-Central) t-Distribution |
| qtNappr |
Compute Approximate Quantiles of the (Non-Central) t-Distribution |
| qtR |
Pure R Implementation of R's C-level t-Distribution Quantiles 'qt()' |
| qtR1 |
Pure R Implementation of R's C-level t-Distribution Quantiles 'qt()' |
| qtU |
'uniroot()'-based Computing of t-Distribution Quantiles |
| qtU1 |
'uniroot()'-based Computing of t-Distribution Quantiles |
| .dntJKBch |
Non-central t-Distribution Density - Algorithms and Approximations |
| .dntJKBch1 |
Non-central t-Distribution Density - Algorithms and Approximations |
| .DT_0 |
Distribution Utilities "dpq" |
| .DT_1 |
Distribution Utilities "dpq" |
| .DT_Cexp |
Distribution Utilities "dpq" |
| .DT_CIv |
Distribution Utilities "dpq" |
| .DT_Clog |
Distribution Utilities "dpq" |
| .DT_Cval |
Distribution Utilities "dpq" |
| .DT_exp |
Distribution Utilities "dpq" |
| .DT_Log |
Distribution Utilities "dpq" |
| .DT_log |
Distribution Utilities "dpq" |
| .DT_qIv |
Distribution Utilities "dpq" |
| .DT_val |
Distribution Utilities "dpq" |
| .D_0 |
Distribution Utilities "dpq" |
| .D_1 |
Distribution Utilities "dpq" |
| .D_Clog |
Distribution Utilities "dpq" |
| .D_Cval |
Distribution Utilities "dpq" |
| .D_exp |
Distribution Utilities "dpq" |
| .D_LExp |
Distribution Utilities "dpq" |
| .D_log |
Distribution Utilities "dpq" |
| .D_Lval |
Distribution Utilities "dpq" |
| .D_qIv |
Distribution Utilities "dpq" |
| .D_val |
Distribution Utilities "dpq" |
| .p1l1ser |
Numerically Stable p1l1(t) = (t+1)*log(1+t) - t |
| .pow |
X to Power of Y - R C API 'R_pow()' |
| .qgammaApprBnd |
Compute (Approximate) Quantiles of the Gamma Distribution |
| .suppHyper |
Compute Hypergeometric Probabilities via Binomial Approximations |
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