moments_cmgnd: Compute the First Four Moments of the CMGND Marginal...

In cmgnd: Constrained Mixture of Generalized Normal Distributions

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.

cmgnd documentation built on Aug. 8, 2025, 6:34 p.m.