| DPQ-package {DPQ} | R Documentation |
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}.
The DESCRIPTION file:
| Package: | DPQ |
| Title: | Density, Probability, Quantile ('DPQ') Computations |
| Version: | 0.5-2 |
| Date: | 2022-06-08 |
| Authors@R: | c(person("Martin","Maechler", role=c("aut","cre"), email="maechler@stat.math.ethz.ch", comment = c(ORCID = "0000-0002-8685-9910")) , person("Morten", "Welinder", role = "ctb", comment = "pgamma C code, see PR#7307, Jan. 2005; further pdhyper()") , person("Wolfgang", "Viechtbauer", role = "ctb", comment = "dtWV(), 2002") , person("Ross", "Ihaka", role = "ctb", comment = "src/qchisq_appr.c") , person("Marius", "Hofert", role = "ctb", comment = "lsum(), lssum()") , person("R-core", email = "R-core@R-project.org", role = "ctb", comment = "src/{dpq.h, algdiv.c, pnchisq.c, bd0.c}") , person("R Foundation", role = "cph", comment = "src/qchisq-appr.c") ) |
| 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}. |
| Depends: | R (>= 3.6.0) |
| Imports: | stats, graphics, methods, utils, sfsmisc (>= 1.1-13) |
| Suggests: | Rmpfr, DPQmpfr (>= 0.3-1), gmp, MASS, mgcv, scatterplot3d, interp |
| SuggestsNote: | MASS::fractions() in ex | mgcv, scatt.., interp: some tests/ |
| License: | GPL (>= 2) |
| Encoding: | UTF-8 |
| URL: | https://specfun.r-forge.r-project.org/, https://r-forge.r-project.org/R/?group_id=611 |
| BugReports: | https://r-forge.r-project.org/tracker/?atid=2462&group_id=611 |
| Author: | Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>), Morten Welinder [ctb] (pgamma C code, see PR#7307, Jan. 2005; further pdhyper()), Wolfgang Viechtbauer [ctb] (dtWV(), 2002), Ross Ihaka [ctb] (src/qchisq_appr.c), Marius Hofert [ctb] (lsum(), lssum()), R-core [ctb] (src/{dpq.h, algdiv.c, pnchisq.c, bd0.c}), R Foundation [cph] (src/qchisq-appr.c) |
| Maintainer: | Martin Maechler <maechler@stat.math.ethz.ch> |
Index of help topics:
Bern Bernoulli Numbers
DPQ-package Density, Probability, Quantile ('DPQ')
Computations
M_LN2 Numerical Utilities - Functions, Constants
algdiv Compute log(gamma(b)/gamma(a+b)) when b >= 8
b_chi Compute E[chi_nu]/sqrt(nu) useful for t- and
chi-Distributions
bd0 Utility Functions for 'dgamma()' - Pure R
Versions
bpser 'pbeta()' 'bpser' series computation
dbinom_raw R's C Mathlib (Rmath) dbinom_raw() Binomial
Probability pure R Function
dgamma.R Gamma Density Function Alternatives
dhyperBinMolenaar HyperGeometric (Point) Probabilities via
Molenaar's Binomial Approximation
dnbinomR Pure R Versions of R's C (Mathlib) dnbinom()
Negative Binomial Probabilities
dnchisqR Approximations of the (Noncentral) Chi-Squared
Density
dntJKBf1 Non-central t-Distribution Density - Algorithms
and Approximations
dpsifn Psi Gamma Functions Workhorse from R's API
dtWV Noncentral t Distribution Density by W.V.
format01prec Format Numbers in [0,1] with "Precise" Result
frexp Base-2 Representation and Multiplication of
Numbers
hyper2binomP Transform Hypergeometric Distribution
Parameters to Binomial Probability
lbetaM (Log) Beta Approximations
lfastchoose R versions of Simple Formulas for Logarithmic
Binomial Coefficients
lgamma1p Accurate 'log(gamma(a+1))'
lgammaAsymp Asymptotic Log Gamma Function
log1mexp Compute log(1 - exp(-a)) and log(1 + exp(x))
Numerically Optimally
log1pmx Accurate 'log(1+x) - x' Computation
logcf Continued Fraction Approximation of Log-Related
Power Series
logspace.add 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)
newton Simple R level Newton Algorithm, Mostly for
Didactical Reasons
p1l1 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
phyper1molenaar Molenaar's Normal Approximations to the
Hypergeometric Distribution
phyperAllBin Compute Hypergeometric Probabilities via
Binomial Approximations
phyperApprAS152 Normal Approximation to cumulative Hyperbolic
Distribution - AS 152
phyperBin.1 HyperGeometric Distribution via Approximate
Binomial Distribution
phyperBinMolenaar 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
pnbetaAppr2 Noncentral Beta Probabilities
pnchi1sq (Probabilities of Non-Central Chi-squared
Distribution for Special Cases
pnchisq (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()
pntR Non-central t Probability Distribution -
Algorithms and Approximations
ppoisErr Direct Computation of 'ppois()' Poisson
Distribution Probabilities
qbetaAppr 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
qgammaAppr Compute (Approximate) Quantiles of the Gamma
Distribution
qnbinomR Pure R Implementation of R's qnbinom() with
Tuning Parameters
qnchisqAppr Compute Approximate Quantiles of Noncentral
Chi-Squared Distribution
qnormAppr Approximations to 'qnorm()', i.e., z_alpha
qnormR Pure R version of R's 'qnorm()' with
Diagnostics and Tuning Parameters
qpoisR Pure R Implementation of R's qpois() with
Tuning Parameters
qtAppr Compute Approximate Quantiles of Non-Central t
Distribution
r_pois Compute Relative Size of i-th term of Poisson
Distribution Series
Further information is available in the following vignettes:
Noncentral-Chisq | Noncentral Chi-Squared Probabilities -- Algorithms in R (source) |
comp-beta | Computing Beta(a,b) for Large Arguments (source) |
log1pmx-etc | log1pmx, bd0, stirlerr - Probability Computations in R (source) |
An important goal is to investigate diverse algorithms and approximations
of R's own density (d*()), probability (p*()), and
quantile (q*()) functions, notably in “border” cases where
the traditional published algorithms have shown to be suboptimal, not
quite accurate, or even useless.
Examples are border cases of the beta distribution, or non-central distributions such as the non-central chi-squared and t-distributions.
Principal author and maintainer: NA
The package DPQmpfr (not yet on CRAN), which builds on this package and on Rmpfr.
## Show problem in R's non-central t-distrib. density (and approximations): example(dntJKBf)