The New Ristić-Balakrishnan-Topp-Leone-Marshall-Olkin-G Family of Distributions with Applications

This study is concerned with the generation of the new flexible family of distributions called Ristić-Balakrishnan-Topp-Leone-Marshall-Olkin-G (RB-TL-MO-G) distribution using gamma generator. Several statistical properties including hazard rate function, quantile function, moments, moments generating function, incomplete and conditional moments, entropy, distribution of order statistics, stochastic orderings are presented. Parameters of the new distribution are estimated using Maximum Likelihood, Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, Cramér-von Mises and Maximum Product of Spacing methods of estimation. Furthermore, the effectiveness of the estimates is assessed through numerical simulation studies. To show the flexibility and adaptability of the new RB-TL-MO-G family of distributions, three real life data sets from various areas are utilized.