nb_sum_exact

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.

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.

Gregory Bedwell

nbconv

Evaluate Arbitrary Negative Binomial Convolutions

nb_sum_exact function

<dl><dt>phis</dt>
<dd>Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.</dd>
<dt>ps</dt>
<dd>Vector of individual probabilities of success.</dd>
<dt>n.terms</dt>
<dd>The number of terms to include in the series for evaluating the PMF at a given number of counts. Defaults to 1000.</dd>
<dt>counts</dt>
<dd>The vector of counts over which the PMF is evaluated.</dd>
<dt>n.cores</dt>
<dd>The number of CPU cores to use in the evaluation. Allows parallelization.</dd>
<dt>tolerance</dt>
<dd>The acceptable difference between the sum of the K distribution and 1.</dd></dl>

Arguments

Furman's PMF — nb_sum_exact

<dl>

<dt>phis</dt>
<dd>Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.</dd>


<dt>ps</dt>
<dd>Vector of individual probabilities of success.</dd>


<dt>n.terms</dt>
<dd>The number of terms to include in the series for evaluating the PMF at a given number of counts. Defaults to 1000.</dd>


<dt>counts</dt>
<dd>The vector of counts over which the PMF is evaluated.</dd>


<dt>n.cores</dt>
<dd>The number of CPU cores to use in the evaluation. Allows parallelization.</dd>


<dt>tolerance</dt>
<dd>The acceptable difference between the sum of the K distribution and 1.</dd>

</dl>

nb_sum_exact: Furman's PMF

Description

Usage

Value

Arguments

Examples