On the Characteristics of the Pseudo-gamma Distribution with Application in Reliability and Medical Sciences
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RESEARCH PAPER
On the Characteristics of the Pseudo-gamma Distribution with Application in Reliability and Medical Sciences Salman Abbas1 • Muhammad Mohsin1 Received: 21 October 2019 / Accepted: 23 July 2020 Ó Shiraz University 2020
Abstract This paper explores several characteristics of the pseudo-gamma (PG) distribution proposed by Mohsin et al. (J Appl Stat Sci 18(2):239–250, 2010) and finds it such a pliable distribution which approaches a variety of well-known distributions. The PG distribution is capable of describing the high probability at tails. An account of reliability features such as survival function, hazard rate function, moments for residual and reversed residual life, and stress-strength analysis is provided. The characterization of the understudy distribution is presented by using conditional moments. An empirical study of mean, variance, skewness, and kurtosis is conducted for different combinations of the parametric values. The maximum likelihood (ML) method is followed to estimate the model parameters. A simulation study of the PG distribution is also conducted for different sample sizes to examine the average ML estimates, standard errors, biases, and corresponding confidence intervals. The potential and feasibility of the PG distribution is supported by its successful application to two real-life data. Keywords Pseudo-gamma distribution Moments Reliability analysis Characterization Empirical study
1 Introduction Statistical models, originated from probability distributions, are vital on account of analyzing and describing the pattern of random variability of data in real life. They measure the variability in a systemic way to handle the complexities and lead toward useful inferences and predictions. The upcoming complex situations always demand continual modifications of the classical models as well as development of new models. In this context, generalization of the probability distributions has been a popular approach to handle the real-life problems effectively. Indeed, the generalization helps to improve the modeling potential of the existing distribution usually by the induction of additional parameters, e.g., location, scale, shape, etc. We possess a sound literature on & Muhammad Mohsin [email protected] Salman Abbas [email protected] 1
the generalization of several distributions. Some prominent generalizations are beta generalized distribution, gamma generated distribution, generalized gamma distribution, Kumaraswamy generalized distribution, McDonald generalized distribution, beta extended Weibull generalized distribution, transformed–transformer (T-X) family of distributions, logistic generalized distribution, beta-Marshall– Olkin generalized distribution, transmuted family of distrubtions, etc., by Eugene et al. (2002), Zografos and Balakrishnan (2009), Khodabina and Ahmadabadib (2010), Cordeiro and de-Castro (2011), Alexander et al. (2012), Cordeiro et al. (2012), Alzaatreh et al. (2013), Torabi and Mon
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