moments_cmgnd {cmgnd}R Documentation

Compute the First Four Moments of the CMGND Marginal Distribution

Description

Computes the mean, variance, skewness, and kurtosis of the marginal distribution of a univariate Constrained Mixture of Generalized Normal Distributions (CMGND) model, given the model parameters.

Usage

moments_cmgnd(parameters)

Arguments

parameters

A matrix or data frame where each row corresponds to a component of the mixture. Columns must be ordered as follows:

1

Mixing proportions \pi_k

2

Component means \mu_k

3

Scale parameters \sigma_k

4

Shape parameters \nu_k

Details

The function assumes that the parameters define a valid CMGND model and uses analytical expressions to compute the first four moments of the marginal distribution. The shape parameter \nu_k governs the kurtosis of each component.

Value

A named list with the following elements:

mean

The marginal mean of the CMGND distribution

var

The marginal variance

skew

The marginal skewness

kur

The marginal kurtosis

See Also

cmgnd for estimating CMGND model parameters.


[Package cmgnd version 0.1.1 Index]