nb_sum_saddlepoint

Implements the saddlepoint approximation for 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_saddlepoint function

<dl><dt>mus</dt>
<dd>Vector of individual mean values.</dd>
<dt>phis</dt>
<dd>Vector of individual dispersion parameters. Equivalent to 'size' in dnbinom.</dd>
<dt>counts</dt>
<dd>The vector of counts over which the PMF is evaluated.</dd>
<dt>normalize</dt>
<dd>Boolean. If TRUE, the PMF is normalized to sum to 1.</dd>
<dt>n.cores</dt>
<dd>The number of CPU cores to use in the evaluation. Allows parallelization.</dd></dl>

Arguments

Saddlepoint approximation — nb_sum_saddlepoint

<dl>

<dt>mus</dt>
<dd>Vector of individual mean values.</dd>


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


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


<dt>normalize</dt>
<dd>Boolean. If TRUE, the PMF is normalized to sum to 1.</dd>


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

</dl>

nb_sum_saddlepoint: Saddlepoint approximation

Description

Usage

Value

Arguments

Details

Examples