Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test
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Unit Modified Burr‑III Distribution: Estimation, Characterizations and Validation Test Muhammad Ahsan ul Haq1,2 · Sharqa Hashmi1,3 · Khaoula Aidi4 · Pedro Luiz Ramos5 · Francisco Louzada5 Received: 30 March 2020 / Revised: 28 April 2020 / Accepted: 26 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, a new three-parameter unit probability distribution is proposed. The new model is a generalization of Burr III distribution, and it is more flexible than some existing well-known distribution due to its different shapes of the hazard function and probability density functions. The mathematical properties of this distribution are presented, including moments, reliability measures, mean residual life, and characterizations, and we also propose a modified Chi squared goodness-of-fit test based on Nikulin–Rao–Robson statistic Y 2 in the presence of complete and censored data. The parameters related to the proposed distribution are estimated using wellknown estimation methods. A numerical simulations study is conducted for reinforcement of the results. In the end, we considered two real datasets to illustrate the applicability of the proposed model. Keywords Burr III distribution · Moments · Estimation · Characterization · Goodness-of-fit test
1 Introduction The use of unit distributions plays a crucial role in modeling proportions that are usually observed in the industry, medical applications, and risk analysis to list a few. The two-parameter distribution that is extensively used for modeling bounded data is the Beta distribution [13]. In this context, several probability distributions have been proposed for handling bounded data sets in different fields. Notable among them are Johnson SB distribution [17], Unit-Logistic distribution proposed [25], Topp-Leone distribution [34], Kumaraswamy distribution [20], Unit-Gompertz distribution [24], Unit-Birnbaum-Saunders distribution [22, 23], Unit-Weibull distribution by [22, 23] and Unit-inverse Gaussian distribution by Ghitany et al. [9]. * Muhammad Ahsan ul Haq [email protected] Extended author information available on the last page of the article
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Annals of Data Science
The modified Bur III (MBIII) distribution was proposed by Ali et al. [2] to model the lifetime data. The authors derived the properties of the new model and discussed its application. Bhatt et al. [5] characterized MBIII distribution based on two truncated moments, elasticity function, and reversed hazard function. Important generalization for the Bur III can be seen in Usman and Haq [35] and Chakraborty et al. [6]. On the other hand, some generalizations of MBIII distribution have been attempted by researchers. For example, Ali and Ahmad [1] introduced transmuted modified Burr III distribution. Haq et al. [16] introduced generalized odd Burr III-G family of distributions, and Mukhtar et al. [26] introduced McDonald modified Burr-III distribution. Let X be a non-negative random variable that follows MBIII distribution, then
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