Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE WEIBULL MARSHALL-OLKIN LOMAX DISTRIBUTION WITH APPLICATIONS TO BLADDER AND HEAD CANCER DATA

  • KUMAR, DEVENDRA (Department of Statistics, Central University of Haryana) ;
  • KUMAR, MANEESH (Department of Statistics, Central University of Haryana) ;
  • ABD EL-BAR, AHMED M.T. (Department of Mathematics, College of Science, Taibah University) ;
  • LIMA, MARIA DO CARMO S. (Department of Statistics, Federal University of Pernambuco)
  • Received : 2020.10.10
  • Accepted : 2020.11.25
  • Published : 2021.09.30
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Abstract

The proposal of new families has been worked out by many authors over recent years. Many ways to generate new families have been developed as the methods of addition, linear combination, composition and, one of the newer, the T-X family of distributions. Using this latter method, Korkmaz et al. (2018) proposed a new class called Weibull Marshall-Olkin-G (WMO-G) family. In the present work, we propose a new distribution, based on the WMO-G family, using the Lomax distribution as baseline, called Weibull Marshall-Olkin Lomax (WMOL) distribution. The hazard rate function of this distribution can be increasing, decreasing, bathtub-shaped, decreasing-increasing-decreasing and unimodal. Some properties of the proposed model are developed. Besides that, we consider method of maximum likelihood for estimating the unknown parameters of the WMOL distribution. We provide a simulation study in order to verify the asymptotic properties of the maximum likelihood estimates. The applicability of the new distribution to modeling real life data is proved by two real data sets.

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