Modified Unit-Half-Normal Distribution with Applications

Abstract

In this article, we introduce a new continuous distribution based on the unit interval. This distribution is generated from a transformation of a random variable with half-normal distribution. We study its basic properties, percentiles, moments and order statistics. Maximum likelihood estimation is applied, and we present a simulation study to observe the behavior of the maximum likelihood estimators. We examine two applications to real proportions datasets, where the new distribution is shown to provide a better fit than other distributions defined in the unit interval.

Keywords

• half-normal distribution
• proportions data
• maximum likelihood estimation