The Type I Half Logistics-Topp-Leone-G Distribution Family: Model, its Properties and Applications

Abstract

A number of new, upgraded, generalized, and extended distribution families have recently been developed to improve the distribution's applicability in a wider domain. The Type I Half Logistics-Topp Leone G family of distribution, otherwise known as (the TIHLTL-G) distribution family, was developed as a new generalized distribution family. Explicit expression, moment generating function, moments, probability weighted moment, hazard function, survival function, quantile function, and order statistics were also derived for the novel family. The exponential distribution was employed as a sub-model, and the novel distribution family provided great flexibility towards some sets of data. The methods of parameter estimation adopted are maximum likelihood (MLE) and maximum products of spacing (MPS) methods. Two data sets were examined, and simulation studies were conducted to exemplify the potential application and adaptability of the novel model compared with some of its existing counterparts. The MPS tends to perform better than the MLE in estimating the model parameters when the sample size is very small, but both did perform excellently when the sample sizes are moderate and large, as obtained in the simulation study. However, both methods of estimation of parameters support the novel model (TIHLTL-G) family of distribution through Akaike information and Bayesian information criterion as the best model.