On the Type I Half Logistic Lomax Distribution with applications

Abstract

In this study, a new four-parameter lifetime distribution called the Topp Leone exponentiated Lomax distribution was introduced. Expansion of density for the probability distribution function and cumulative density function was done from which some of the properties of the new model were derived. Some mathematical properties of the distribution such as the moments, moment generating function, quantile function, survival function and hazard function were presented. The probability density function of the maximum and minimum order statistics was also derived and studied. Estimation of the parameters by maximum likelihood method was discussed and used to estimate the unknown parameters of the distribution.  Four real life data sets were used to show the fit and flexibility of the new distribution over some existing lifetime distributions in literature and the results show that the new distribution fits better in the four data sets considered.