Record-Based Transmuted Kumaraswamy Generalized Family of Distributions: Properties and Application

Abstract

The Kumaraswamy distribution is one among the important probability models in applied sciences and has been extensively utilized in the analysis of hydrological data. Due to its similarity with two-parameter beta-type distributions, Kumaraswamy’s densities are also unimodal, increasing, decreasing, or constant depending on its parameters. Recently, Balakrishnan and He (2021) proposed a record-based transmuted map to generate more flexible models for real data analysis. In this chapter, we propose a record-based transmuted generalized family of Kumaraswamy (RTGK) distributions. This class of RTGK distributions provides several new probability models by considering the different baseline models. In particular, we study the statistical properties of record-based transmuted Kumaraswamy (RTK) distribution by considering Kumaraswamy distribution as a baseline distribution in a record-based transmuted model. We also obtained maximum likelihood estimates of the unknown quantities of the proposed distribution. Further, a computational study is provided to discuss the numerical aspects of derived results. Further a real dataset is provided to discuss the application aspect of the proposed distribution. © 2023 Mir Masoom Ali, Irfan Ali, Haitham M. Yousof and Mohamed Ibrahim.