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The Weibull Marshall-Olkin Lomax distribution with applications to bladder and head cancer data. (English) Zbl 1513.62026

Summary: 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, M. Ç. Korkmaz et al. [Commun. Stat., Theory Methods 48, No. 16, 4171–4194 (2019; Zbl 1508.62049)] 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.

MSC:

62E15 Exact distribution theory in statistics
60E05 Probability distributions: general theory
62N05 Reliability and life testing
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 1508.62049
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References:

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