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Calculate the Normalizing Constant in log scale for COM-Poisson distribution

Source: R/Z.R
logZ.Rd

A function to approximate the normalizing constant for COM-Poisson distributions via truncation. The standard COM-Poisson parametrization is being used here.

Usage

logZ(log_lambda, nu, summax = 100)

Arguments

log_lambda

rate parameter in log scale.

nu

dispersion parameter, straightly positive.

summax

maximum number of terms to be considered in the truncated sum.

Value

A numeric vector giving the (approximate) log of the COM-Poisson normalizing constant \(\log Z(\lambda, \nu)\), recycled to the length of the longer of log_lambda and nu.

Details

As of version 0.2.0 of this package, logZ will supersede Z for calculating the normalizing constant. logZ utilised a method that can calculate log(exp(logx) + exp(logy)) in a somewhat numerically stable way.

This function was originally purposed in the cmpreg package of Ribeiro Jr, Zeviani & Demétrio (2019).

References

Ribeiro Jr, E. E., Zeviani, W. M., Demétrio, C. G. B. (2019) cmpreg: Reparametrized COM-Poisson Regression Models. R package version 0.0.1.