A modification in generalized classes of distributions: A new Topp–Leone class as an example

Ali, Zeeshan; Ali, Azeem; Ozel, Gamze

Abstract

In this article, we have proposed a wider class of distributions by modifying the distribution function of the baseline density. This new class is a generalization of many well–known generators such as beta family, Kumaraswamy family, Kummer beta generalized family and Topp–Leone family. Furthermore, we have introduced a subcase, known as G–Fixed–Topp–Leone class, with different properties and have provided the expression for the reliability in the multicomponent stress–strength model. Additionally, we have studied the exponential–fixed–Topp–Leone distribution as an example; some structural properties of this three-parameter exponential distribution are driven which also include the derivations of incomplete moments, mean deviation, measures of uncertainty, reliability in multicomponent stress-stress model, order statistics, Lorenz, Bonferroni and Zenga curves. The estimation of the unknown parameters is done by the method of maximum likelihood. We have also included a real-life application of this new three-parameter exponential distribution to two datasets. A numerical study for the reliability in the multicomponent stress–strength model for the exponential–fixed–Topp–Leone distribution, using the Markov Chain and Monte Carlo (MCMC) method, is also performed.

Citation

Ali, Z., Ali, A., & Ozel, G. (2021). A modification in generalized classes of distributions: A new Topp–Leone class as an example. Communications in Statistics - Theory and Methods, 50(19), 4548-4570. https://doi.org/10.1080/03610926.2020.1719419

• Journal Article Type: Article
• Acceptance Date: Jan 13, 2020
• Online Publication Date: Feb 17, 2020
• Publication Date: Jan 1, 2021
• Deposit Date: Jul 29, 2024
• Journal: Communications in Statistics - Theory and Methods
• Print ISSN: 0361-0926
• Electronic ISSN: 1532-415X
• Publisher: Taylor and Francis Group
• Peer Reviewed: Peer Reviewed
• Volume: 50
• Issue: 19
• Pages: 4548-4570
• DOI: https://doi.org/10.1080/03610926.2020.1719419
• Keywords: Beta family; Kumaraswamy family; Kummer beta generalized family; Topp–Leone family; Topp–Leone exponential distribution; Reliability in the multicomponent stress–strength model; MCMC
• Public URL: https://hull-repository.worktribe.com/output/4747886