Generalized Topp-Leone family of distributions

Abstract

Background & Aim: Adding parameters to an existing distribution to expand the family of distributions is a very common approach for developing more flexible models. Several ways for generating new distributions from classic ones have been developed. Methods & Materials: A generalization of Topp-Leone generator of distributions was introduced. Several of its fundamental properties were obtained such as quantiles, moments, moment generating function (MGF), order statistics and maximum likelihood estimator (MLE). Results: We provided four sub-models of the new family which extended some of the basic lifetime models such as exponential, Weibull, gamma and generalized exponential distributions. These distributions exhibited a wide range of shapes varying skewness and different forms of hazard rate function (HRF). Conclusion: We have provided four new distributions. The flexibility of the proposed distributions and increased range of skewness were able to fit and capture features in one real dataset much better than some competitor distributions.

Keywords

• Statistical distributions
• Likelihood functions
• Survival analysis