A Comprehensive Simulation Study to Compare Various Estimators of the Model Parameters, Model Mean, as well as Model Percentiles of a Two-Parameter Generalized Half-Normal Distribution (2P-GHND) with Applications

Abstract

This work deals with studying various point estimators of the model parameters, the model mean, as well as the model percentiles of a two-parameter generalized half normal distribution (2P-GHND). First, we study three types of estimators of the model parameters, namely - the method of moments
estimators (MMEs), the maximum likelihood estimators (MLEs), and the ordinary regression estimators (OREs). Then, these three methods are used to obtain the corresponding estimators of the model mean as well as the model percentiles. The estimators have been compared in terms of relative bias (RB) and relative mean squared error (RMSE). Though our primary objective here is to study the small sample behaviour of the estimators, we have also studied the asymptotic behaviour of the MLEs. It has been shown that the MLEs perform far better than the other types of estimators for sample sizes up to 25. For larger sample sizes, all the estimators have nearly similar behaviour. Also, for the MLEs of all the parameters considered in this study, their MSEs can be approximated fairly
well by the respective asymptotic variances obtained from the Fisher information matrix. Finally, we provide asymptotic interval estimates of all the parameters considered here, and show the goodness of fit of 2P-GHND over other commonly used skewed distributions for two real-life datasets.