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.
Highlights
In recent years, for data with positive support, lifetime, or reliability, the half-normal (HN) model has been widely used
In this sub-section we study some properties of the modified slashed half-normal (MSHN) distribution
Note that the MSHN distribution presents higher asymmetry and kurtosis values than the in both distributions when q → ∞ the coefficients of asymmetry and kurtosis converge to 2(4 − π )(π − 2)−3/2 and (3π 2 − 4π − 12)(π − 2)−2, respectively; they coincide with the coefficients of the HN distribution
Summary
For data with positive support, lifetime, or reliability, the half-normal (HN) model has been widely used. The principal goal of this article is to use the idea published by Reyes et al [8] to construct an extension of the half-normal model with a greater range in the coefficient of kurtosis than the SHN model, in order to use it to model atypical data. This will allow us obtain a new model generated on the basis of a scale mixture between an HN and a Weibull (Wei) distribution.
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