Some Inferential Results on a Two Parameter Generalized Half Normal Distribution

Abstract

A two-parameter generalized half normal distribution (2 P-GHND) is gaining attention lately due to its flexibility over other popular distributions on the positive side of the real line. Unlike gamma, lognormal or inverse Gaussian distributions, 2 P-GHND can be either negatively or positively skewed depending on its shape parameter, a property similar to Weibull distribution. In this work we address two inferential problems related to 2 P-GHND: (a) prove analytically the existence and uniqueness of the MLE of the model parameters attained through differentiation of the log-likelihood function; and (b) consider the hypothesis testing on the mean of the distribution where it is shown that a parametric bootstrap (PB) method based on the likelihood ratio test (LRT) statistic works far better than the other asymptotic tests for small to moderate sample sizes. Extensive simulation results have been provided to support this observation.

KEYWORDS AND PHRASES:

• Asymptotic normality
• maximum likelihood estimator
• power
• scale parameter
• shape parameter
• size

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F03
• 62B05
• 62E20