ecp_kmoment {ecpdist}R Documentation

The k-th raw moment of extended Chen-Poisson distribution

Description

Computes the k-th raw moment of the extended Chen-Poisson (ecp) distribution.

Usage

ecp_kmoment(k, lambda, gamma, phi)

Arguments

k

a positive integer.

lambda, gamma

parameter values > 0.

phi

parameter value != 0.

Details

To obtain the value of k-th raw moment of the Extended Chen-Poisson distribution, it is necessary to use numerical integration. For that purpose, the R function 'integrate()' can be used, which returns the estimated value of the integral and also the integral absolute error (see details about function 'integrate()'). Therefore, to obtain the variance, the first component of each k-th raw moments must be selected.

Value

Estimated value of k-th raw moment, based on numerical integration, as well as integral absolute error obtained from the function integrate.

Examples

ecp_kmoment(k = 1, lambda = .1, gamma = .5, phi = - .2) # First raw moment.
ecp_kmoment(k = 2, lambda = .1, gamma = .5, phi = - .2) # Second raw moment.
ecp_kmoment(k = 2, lambda = .1, gamma = .5, phi = - .2)[1] -
ecp_kmoment(k = 1, lambda = .1, gamma = .5, phi = - .2)[1]^2 # Variance.


[Package ecpdist version 0.2.1 Index]