| Title: | Evaluate Arbitrary Negative Binomial Convolutions |
| Version: | 1.0.1 |
| URL: | https://github.com/gbedwell/nbconv |
| BugReports: | https://github.com/gbedwell/nbconv/issues |
| Imports: | parallel, matrixStats, stats |
| Description: | Three distinct methods are implemented for evaluating the sums of arbitrary negative binomial distributions. These methods are: Furman's exact probability mass function (Furman (2007) <doi:10.1016/j.spl.2006.06.007>), saddlepoint approximation, and a method of moments approximation. Functions are provided to calculate the density function, the distribution function and the quantile function of the convolutions in question given said evaluation methods. Functions for generating random deviates from negative binomial convolutions and for directly calculating the mean, variance, skewness, and excess kurtosis of said convolutions are also provided. |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.0 |
| License: | GPL (≥ 3) |
| NeedsCompilation: | no |
| Packaged: | 2023-07-06 18:01:40 UTC; gbedwell |
| Author: | Gregory Bedwell 
[aut, cre, cph] |
| Maintainer: | Gregory Bedwell <gregoryjbedwell@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2023-07-06 18:20:02 UTC |
Probability mass function
Description
Calculates the PMF for the convolution of arbitrary negative binomial random variables.
Usage
dnbconv(
counts,
mus,
ps,
phis,
method = c("exact", "moments", "saddlepoint"),
n.terms = 1000,
n.cores = 1,
tolerance = 0.001,
normalize = TRUE
)
Arguments
counts |
The counts over which the convolution is evaluated. Should be a vector. |
mus |
Vector of individual mean values |
ps |
Vector of individual probabilities of success. |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
method |
The method by which to evaluate the PMF. One of "exact", "moments", or "saddlepoint". |
n.terms |
The number of terms to include in the series for evaluating the PMF at a given number of counts. Defaults to 1000. |
n.cores |
The number of CPU cores to use in the evaluation. Allows parallelization. |
tolerance |
The acceptable difference between the sum of the K distribution and 1. |
normalize |
Boolean. If TRUE, the PMF is normalized to sum to 1. |
Value
A numeric vector of probability densities.
Examples
dnbconv(counts = 0:500, mus = c(100, 10), phis = c(5, 8), method = "exact")
Furman's PMF
Description
Implements Furman's exact PMF for the evaluation of the sum of arbitrary NB random variables. Called by other functions. Not intended to be run alone.
Usage
nb_sum_exact(phis, ps, n.terms = 1000, counts, n.cores = 1, tolerance = 0.001)
Arguments
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
ps |
Vector of individual probabilities of success. |
n.terms |
The number of terms to include in the series for evaluating the PMF at a given number of counts. Defaults to 1000. |
counts |
The vector of counts over which the PMF is evaluated. |
n.cores |
The number of CPU cores to use in the evaluation. Allows parallelization. |
tolerance |
The acceptable difference between the sum of the K distribution and 1. |
Value
A numeric vector of probability densities.
Examples
nb_sum_exact(ps = c(0.05, 0.44), phis = c(5, 8), counts = 0:500)
Method of moments
Description
Implements the method of moments approximation for the sum of arbitrary NB random variables. Called by other functions. Not intended to be run alone.
Usage
nb_sum_moments(mus, phis, counts)
Arguments
mus |
Vector of individual mean values. |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
counts |
The vector of counts over which the PMF is evaluated. |
Value
A numeric vector of probability densities.
Examples
nb_sum_moments(mus = c(100, 10), phis = c(5, 8), counts = 0:500)
Saddlepoint approximation
Description
Implements the saddlepoint approximation for the sum of arbitrary NB random variables. Called by other functions. Not intended to be run alone.
Usage
nb_sum_saddlepoint(mus, phis, counts, normalize = TRUE, n.cores = 1)
Arguments
mus |
Vector of individual mean values. |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
counts |
The vector of counts over which the PMF is evaluated. |
normalize |
Boolean. If TRUE, the PMF is normalized to sum to 1. |
n.cores |
The number of CPU cores to use in the evaluation. Allows parallelization. |
Details
Inspired by https://www.martinmodrak.cz/2019/06/20/approximate-densities-for-sums-of-variables-negative-binomials-and-saddlepoint/
Value
A numeric vector of probability densities.
Examples
nb_sum_saddlepoint(mus = c(100, 10), phis = c(5, 8), counts = 0:500)
Summary statistics
Description
Calculates distribution parameters for the convolution of arbitrary negative binomial random variables.
Usage
nbconv_params(mus, phis, ps)
Arguments
mus |
Vector of individual mean values |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
ps |
Vector of individual probabilities of success. |
Value
A named numeric vector of distribution parameters.
Examples
nbconv_params(mus = c(100, 10), phis = c(5, 8))
Cumulative distribution function
Description
Calculates the CDF for the convolution of arbitrary negative binomial random variables.
Usage
pnbconv(
quants,
mus,
ps,
phis,
method = c("exact", "moments", "saddlepoint"),
n.terms = 1000,
n.cores = 1,
tolerance = 0.001,
normalize = TRUE
)
Arguments
quants |
Vector of quantiles. |
mus |
Vector of individual mean values |
ps |
Vector of individual probabilities of success. |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
method |
The method by which to evaluate the PMF. One of "exact", "moments", or "saddlepoint". |
n.terms |
The number of terms to include in the series for evaluating the PMF at a given number of counts. Defaults to 1000. |
n.cores |
The number of CPU cores to use in the evaluation. Allows parallelization. |
tolerance |
The acceptable difference between the sum of the K distribution and 1. |
normalize |
Boolean. If TRUE, the PMF is normalized to sum to 1. |
Value
A numeric vector of cumulative probability densities.
Examples
pnbconv(quants = 200, mus = c(100, 10), phis = c(5, 8), method = "exact")
Quantile function
Description
Calculates the quantile function for the convolution of arbitrary negative binomial random variables.
Usage
qnbconv(
probs,
counts,
mus,
ps,
phis,
method = c("exact", "moments", "saddlepoint"),
n.terms = 1000,
n.cores = 1,
tolerance = 0.001,
normalize = TRUE
)
Arguments
probs |
Vector of target (cumulative) probabilities. |
counts |
Vector of counts over which the PMF is evaluated. |
mus |
Vector of individual mean values |
ps |
Vector of individual probabilities of success. |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
method |
The method by which to evaluate the PMF. One of "exact", "moments", or "saddlepoint". |
n.terms |
The number of terms to include in the series for evaluating the PMF at a given number of counts. Defaults to 1000. |
n.cores |
The number of CPU cores to use in the evaluation. Allows parallelization. |
tolerance |
The acceptable difference between the sum of the K distribution and 1. |
normalize |
Boolean. If TRUE, the PMF is normalized to sum to 1. |
Value
A numeric vector of quantiles.
Examples
qnbconv(probs = c(0.05, 0.25, 0.5, 0.75, 0.95), counts = 0:500,
mus = c(100, 10), phis = c(5, 8), method = "exact")
Random deviates
Description
Generates random samples from the convolution of arbitrary negative binomial random variables.
Usage
rnbconv(mus, phis, ps, n.samp, n.cores = 1)
Arguments
mus |
Vector of individual mean values |
phis |
Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom. |
ps |
Vector of individual probabilities of success. |
n.samp |
The number of samples per distribution |
n.cores |
The number of CPU cores to use in the evaluation. Allows parallelization. |
Value
A numeric vector of random deviates.
Examples
rnbconv(mus = c(100, 10), phis = c(5, 8), n.samp = 10)