Joint Modelling of Location, Scale and Skewness Parameters of the Skew Laplace Normal Distribution

TL;DR

This paper introduces a joint modeling approach for location, scale, and skewness parameters of the skew Laplace normal distribution, providing an alternative to skew-t-normal models for asymmetric and heavy-tailed data.

Contribution

It develops maximum likelihood estimators for the joint parameters of the SLN distribution using EM algorithm, with validation through simulations and real data.

Findings

The EM algorithm effectively estimates parameters of the SLN model.

The model performs well on simulated data with heavy tails and skewness.

Application to real data demonstrates practical utility.

Abstract

In this article, we propose joint location, scale and skewness models of the skew Laplace normal (SLN) distribution as an alternative model for joint modelling location, scale and skewness models of the skew-t-normal (STN) distribution when the data set contains both asymmetric and heavy-tailed observations. We obtain the maximum likelihood (ML) estimators for the parameters of the joint location, scale and skewness models of the SLN distribution using the expectation-maximization (EM) algorithm. The performance of the proposed model is demonstrated by a simulation study and a real data example.