Package 'nbconv' reference manual

Title:	Evaluate Arbitrary Negative Binomial Convolutions
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.
Authors:	Gregory Bedwell [aut, cre, cph]
Maintainer:	Gregory Bedwell <[email protected]>
License:	GPL (>= 3)
Version:	1.0.1
Built:	2024-11-16 16:15:23 UTC
Source:	https://github.com/gbedwell/nbconv

Probability Mass Function

Description

Calculates the probability mass function 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
)
dnbconv(
  counts,
  mus,
  ps,
  phis,
  method = c("exact", "moments", "saddlepoint"),
  n.terms = 1000,
  n.cores = 1,
  tolerance = 0.001,
  normalize = TRUE
)

Arguments

`counts`	Integer vector of counts over which the convolution is evaluated.
`mus`	Numeric vector of individual mean values
`ps`	Numeric vector of individual probabilities of success.
`phis`	Numeric 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 representation of the exact PMF. 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. Defaults to 1E-3.
`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")

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)
nb_sum_exact(phis, ps, n.terms = 1000, counts, n.cores = 1, tolerance = 0.001)

Arguments

`phis`	Numeric vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.
`ps`	Numeric vector of individual probabilities of success.
`n.terms`	The number of terms to include in the series representation of the exact PMF. Defaults to 1000.
`counts`	Integer vector of counts over which the convolution 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. Defaults to 1E-3.

Value

A numeric vector of probability densities.

Examples

nb_sum_exact(ps = c(0.05, 0.44), phis = c(5, 8), counts = 0:500)

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)
nb_sum_moments(mus, phis, counts)

Arguments

`mus`	Numeric vector of individual mean values
`phis`	Numeric vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.
`counts`	Integer vector of counts over which the convolution is evaluated.

Value

A numeric vector of probability densities.

Examples

nb_sum_moments(mus = c(100, 10), phis = c(5, 8), counts = 0:500)

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)
nb_sum_saddlepoint(mus, phis, counts, normalize = TRUE, n.cores = 1)

Arguments

`mus`	Numeric vector of individual mean values
`phis`	Numeric vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.
`counts`	Integer vector of counts over which the convolution 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.

Value

A numeric vector of probability densities.

Examples

nb_sum_saddlepoint(mus = c(100, 10), phis = c(5, 8), counts = 0:500)

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)
nbconv_params(mus, phis, ps)

Arguments

`mus`	Numeric vector of individual mean values
`phis`	Numeric vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.
`ps`	Numeric 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))

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
)
pnbconv(
  quants,
  mus,
  ps,
  phis,
  method = c("exact", "moments", "saddlepoint"),
  n.terms = 1000,
  n.cores = 1,
  tolerance = 0.001,
  normalize = TRUE
)

Arguments

`quants`	Integer vector of quantiles.
`mus`	Numeric vector of individual mean values
`ps`	Numeric vector of individual probabilities of success.
`phis`	Numeric 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 representation of the exact PMF. 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")

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
)
qnbconv(
  probs,
  counts,
  mus,
  ps,
  phis,
  method = c("exact", "moments", "saddlepoint"),
  n.terms = 1000,
  n.cores = 1,
  tolerance = 0.001,
  normalize = TRUE
)

Arguments

`probs`	Numeric vector of target (cumulative) probabilities.
`counts`	Integer vector of counts over which the PMF is evaluated.
`mus`	Numeric vector of individual mean values
`ps`	Numeric vector of individual probabilities of success.
`phis`	Numeric 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 representation of the exact PMF. 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. Defaults to 1E-3.
`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")

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)
rnbconv(mus, phis, ps, n.samp, n.cores = 1)

Arguments

`mus`	Numeric vector of individual mean values
`phis`	Numeric vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.
`ps`	Numeric vector of individual probabilities of success.
`n.samp`	The number of samples per distribution
`n.cores`	The number of 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)

rnbconv(mus = c(100, 10), phis = c(5, 8), n.samp = 10)

Package 'nbconv'

Help Index

Probability Mass Function

Description

Usage

Arguments

Value

Examples

Furman's PMF

Description

Usage

Arguments

Value

Examples

Method of Moments

Description

Usage

Arguments

Value

Examples

Saddlepoint approximation

Description

Usage

Arguments

Value

Examples

Summary statistics

Description

Usage

Arguments

Value

Examples

Cumulative Distribution Function

Description

Usage

Arguments

Value

Examples

Quantile Function

Description

Usage

Arguments

Value

Examples

Random Deviates

Description

Usage

Arguments

Value

Examples