Abstract
ABSTRACT The Half-Normal distribution has been intensively extended in the recent years. A review of the literature showed that at least 10 extensions of the Half-Normal distribution were introduced between 2008 and 2016. These extensions generalized the behavior of the density and hazard functions, which are restricted to monotonous decreasing and monotonically increasing, respectively. In this paper we propose a new extension called the transmuted Half-Normal distribution using the quadratic rank transmutation map, introduced by Shaw & Buckley (2009). A comprehensive account of mathematical properties of the new distribution is presented. We provide explicit expressions for the moments, moment-generating function, Shannon’s entropy, mean deviations, Bonferroni and Lorenz curves, order statistics, and reliability. The estimation of the parameters is implemented by the maximum likelihood method. The bias and accuracy of the estimators are assayed by the Monte Carlo simulations. This proposed distribution allows us to incorporate covariates directly in the mean and consequently to quantify their influences on the average of the response variable. Experiment with two real data sets show usefulness and its value as a good alternative to several extensions of the Half-Normal distribution in data modeling with and without covariates.
Highlights
Underlying any parametric inference procedure a probability distribution is used to describe the behavior of a random variable in the population
We present the transmuted Half-Normal distribution (THN) distribution formulated from the quadratic transmutation proposed by Shaw & Buckley (2009)
It is important to note that the moment generating function, moment of order k, mean, variance, asymmetry and kurtosis have explicit analytic expressions, which depend only of the parameters of the THN distribution
Summary
Underlying any parametric inference procedure a probability distribution is used to describe the behavior of a random variable in the population. Many strategies can be used to generate or extend a probability distribution Most of these strategies adds one or more parameters to some basic distribution (Normal, Gumbel, Exponential, Weibull, Range, Log-Normal, among many others). It is important to emphasize that the transformation of a random variable Z into another X, of the form X = g(Z), is the simplest way to generate or extend a base probability distribution. In the recent years several extensions of the HalfNormal distribution were proposed. This article introduces the transmuted Half-Normal distribution (THN), derived from the HN distribution.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
