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]