Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

Abstract

In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.

Some Inferences on Three Parameters Birnbaum-Saunders Distribution: Statistical Properties, Characterizations and Applications

“…In this paper, we consider data from two real-world problems in the context of parameter estimation. Some more examples on parameter estimation as given in [31,32,33,34,35] can be considered by this method. In this sub-section, by considering two real-world data set examples, the goodness of fit tests of BS (3P) distribution is provided by comparing it with some well-known skew distributions, namely, BS (2P), log-logistic, lognormal, generalized extreme value, inverse Gaussian, and Weibull distributions.…”