Indian Journal of Pure and Applied Mathematics

, Volume 49, Issue 4, pp 633–650

# Statistical Inference for the Location and Scale Parameters of the Skew Normal Distribution

• Wenhao Gui
• Lei Guo
Article

## Abstract

In this paper, we consider the problem of estimating the location and scale parameters of the skew normal distribution introduced by Azzalini. For this distribution, the classic maximum likelihood estimators(MLEs) do not take explicit forms. We approximate the likelihood equations and derive explicit estimators of the parameters. The bias and variance of the estimators are investigated and Monte Carlo simulation studies show that the estimators are as efficient as the classic MLEs. We demonstrate that the probability coverages of the pivotal quantities (for location and scale parameters) based on asymptotic normality are unsatisfactory, especially when the sample size is small. The use of unconditional simulated percentage points of these quantities is suggested. Finally, a numerical example is used to illustrate the proposed inference methods.

## Key words

Skew normal distribution maximum-likelihood estimator Monte Carlo simulation probability coverage pivotal quantity

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