Abstract
A new class of distributions called Marshall-Olkin Zubair-G family is proposed in this study. Some statistical properties of the family are derived and two special distributions namely, Marshall-Olkin Zubair Nadarajah-Haghighi and Marshall-Olkin Zubair Weibull distributions are developed. The plots of the density and hazard rate functions of the special distributions exhibit different shapes for chosen parameter values, making them good candidates for modeling different types of datasets. A real life application using the Marshall-Olkin Zubair Nadarajah-Haghighi distribution revealed that it performs better than other existing extensions of the Nadarajah-Haghighi distribution for the given dataset.
Highlights
The quest to develop flexible probability distributions have become an issue of interest to myriad of researchers owing to the usefulness of these distributions in modeling datasets and making inference in areas such as engineering, financial and biological modeling among others
Some common generators that have been developed for modifying existing distributions include: Marshall-Olkin alpha power family (Nassar et al, 2019); extended odd Fréchet-G family (Nasiru, 2018); Marshall-Olkin extended family (Marshall and Olkin, 1997); Zubair-G family (Zubair, 2018); Kumaraswamy-G family (Cordeiro and de Castro, 2011); odd Fréchet-G family (Haq and Elgarhy, 2018); odd Burr-G Poisson family (Nasir et al, 2018); alpha power transformed family (Mahdavi and Kundu, 2017); exponentiated generalized transformed-transformer family (Nasiru et al, 2017), Marshall-Olkin extended generalized Rayleigh (MirMostafaee et al, 2017) and Marshall-Olkin Burr X family (Jamal et al, 2017)
The objective of this study is to develop another extension of the Zubair-G family called Marshall-Olkin Zubair (MOZ)-G family by adding an extra shape parameter to the Zubair-G family to make it more flexible
Summary
The quest to develop flexible probability distributions have become an issue of interest to myriad of researchers owing to the usefulness of these distributions in modeling datasets and making inference in areas such as engineering, financial and biological modeling among others. A physical interpretation of the new family is as follows: given N independent components each with probability mass function P(N = n) = (1− )n−1, n = 1, 2,... Suppose the lifetime of each component X1, X2,..., X N are independent and identically distributed Zubair-G random variables with parameters and. The CDF in equation (3) can be interpreted as follows: suppose the random variable N with probability mass function. The mixture representation of the density function is useful when deriving the structural properties of the MOZ-G family of distributions
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