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


Ali Z., Ali A., Ozel G.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.50, no.19, pp.4548-4570, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 50 Issue: 19
  • Publication Date: 2021
  • Doi Number: 10.1080/03610926.2020.1719419
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.4548-4570
  • Keywords: Beta family, Kumaraswamy family, Kummer beta generalized family, Topp-Leone family, Topp-Leone exponential distribution, reliability in the multicomponent stress-strength model, MCMC, FAMILY, RELIABILITY, MOMENTS
  • Hacettepe University Affiliated: Yes

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.