An Asymmetric Distribution with Heavy Tails and Its Expectation–Maximization (EM) Algorithm Implementation

Abstract

In this paper we introduce a new distribution constructed on the basis of the quotient of two independent random variables whose distributions are the half-normal distribution and a power of the exponential distribution with parameter 2 respectively. The result is a distribution with greater kurtosis than the well known half-normal and slashed half-normal distributions. We studied the general density function of this distribution, with some of its properties, moments, and its coefficients of asymmetry and kurtosis. We developed the expectation–maximization algorithm and present a simulation study. We calculated the moment and maximum likelihood estimators and present three illustrations in real data sets to show the flexibility of the new model.

A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

“…Specifically, for α = 0 and θ = (2σ) −1 , the MSGR model is reduced to the modified slashed Rayleigh distribution [27]. If α = −1/2 and θ = (2σ 2 ) −1 , then the MSGR reduces to the modified slashed half-normal distribution [28]. For α = 1/2 and θ = σ/2, we get the modified slashed Maxwell distribution.…”

A Power Maxwell Distribution with Heavy Tails and Applications

“…Reference Iriarte et al [8] and Gómez et al [9] used this methodology to extend the generalized Rayleigh distribution and Gumbel respectively. Reference Olmos et al [10] also used this methodology to introduce the modified slashed half-normal distribution. Reference Olmos et al [11] recently introduced the confluent, hypergeometric slashed-Rayleigh distribution using the same methodology.…”