Order Statistics and Their Linear Combinations for the Power Half Normal Distribution

Abstract

The power half normal distribution is an extension of the traditional half normal distribution. It introduces a power parameter to the half normal distribution for greater flexibility when modelling skewed data and data with varying tail behaviour. This paper looks at the underlying properties of the power half normal distribution, including the moments, the hazard rate, reliability functions and then the order statistics are introduced along with the L moments of the distribution. The methods are then demonstrated on a real dataset.