moments_cmgnd

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.

The 'cmgnd' implements the constrained mixture of generalized normal distributions model, a flexible statistical framework for modelling univariate data exhibiting non-normal features such as skewness, multi-modality, and heavy tails. By imposing constraints on model parameters, the 'cmgnd' reduces estimation complexity while maintaining high descriptive power, offering an efficient solution in the presence of distributional irregularities. For more details see Duttilo and Gattone (2025) <doi:10.1007/s00180-025-01638-x> and Duttilo et al (2025) <doi:10.48550/arXiv.2506.03285>.

Pierdomenico Duttilo

cmgnd

Constrained Mixture of Generalized Normal Distributions

Stefano Antonio Gattone

Alfred Kume

moments_cmgnd function

<dl><dt>parameters</dt>
<dd>A matrix or data frame where each row corresponds to a component
of the mixture. Columns must be ordered as follows:<dl>
 <dt>1</dt>
<dd>Mixing proportions \(\pi_k\)</dd></dl></dd> <dt>2</dt>
<dd>Component means \(\mu_k\)</dd> <dt>3</dt>
<dd>Scale parameters \(\sigma_k\)</dd> <dt>4</dt>
<dd>Shape parameters \(\nu_k\)</dd>
</dl>

Arguments

Compute the First Four Moments of the CMGND Marginal Distribution — moments_cmgnd

<dl>

<dt>parameters</dt>
<dd>A matrix or data frame where each row corresponds to a component
of the mixture. Columns must be ordered as follows:<dl>
 <dt>1</dt>
<dd>Mixing proportions \(\pi_k\)</dd>

 <dt>2</dt>
<dd>Component means \(\mu_k\)</dd>

 <dt>3</dt>
<dd>Scale parameters \(\sigma_k\)</dd>

 <dt>4</dt>
<dd>Shape parameters \(\nu_k\)</dd>


</dl></dd>

</dl>

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

Description

Usage

Value

Arguments

Details

See Also