compoisson (version 0.3)

com.log.density: Computes the Log PMF of the COM-Poisson Distribution

Description

Computes the log probability mass function of the COM-Poisson distribution for given values of the parameters.

Usage

com.log.density(x, lambda, nu, log.z = NULL)

Arguments

x

level to evaulate the log PMF at

lambda

value of the lambda parameter

nu

value of the nu parameter

log.z

log of the normalizing constant, computed if not specified

Value

The log probability that a random COM-Poisson variable X takes value x.

Details

Computes the log probability mass function of the COM-Poisson distribution $$ \log f(x) = x \log \lambda - \log(Z(\lambda,\nu)) - \nu \sum_{i=1}^x x. $$

References

Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S. and Boatwright, P., “A useful distribution for fitting discrete data: Revival of the Conway-Maxwell-Poisson distribution,” J. Royal Statist. Soc., v54, pp. 127-142, 2005.

See Also

com.loglikelihood, dcom

Examples

	data(insurance);
	fit = com.fit(Lemaire);
	com.log.density(0, fit$lambda, fit$nu, fit$z);