The information matrix of the bivariate extended skew-normal distribution

TL;DR

This paper derives explicit formulas for the score function and information matrix of the bivariate extended skew-normal distribution, enhancing understanding of its properties and providing practical R code implementations.

Contribution

It provides the first explicit derivations of the score function and information matrix for the bivariate extended skew-normal distribution, filling a gap in the literature.

Findings

Explicit expressions for the score function derived.

Explicit expressions for the information matrix derived.

R code implementation provided.

Abstract

For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we derive explicit expressions for the score function and the information matrix, in the observed and the expected form; these do not appear to have been examined before in the literature. Corresponding computing code in R language is provided, which implements the formal expressions.