Unit Half Logistic Normal Distribution: Properties and Applications

Abstract

In this study, a new generalization of the normal distribution called the unit half logistic normal (UHLN) distribution has been proposed by introducing a shape parameter into the normal distribution to make it more flexible. Several statistical properties of the new distribution which include; the cumulative hazard function, reversed hazard function, hazard rate average function, quantile function, moments, moment generating function and order statistics has been derived. Estimators such as the maximum likelihood, ordinary least squares, weighted least squares and Cramér-von Mises were developed for the new model. The performances of the estimators were investigated via Monte Carlo simulation using six different sample sizes and replicated 5000 times. The maximum likelihood was observed to be the most consistent and the best technique, hence was used to estimate the parameters of the new distribution. The applications of the UHLN distribution was demonstrated using three different datasets and compared with the normal, transmuted normal, beta normal, McDonal normal and logistic distributions. The results revealed that the UHLN distribution performs better for the given datasets.