Abstract
Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type‐II (MOEGT‐II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J‐shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT‐II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT‐II distribution have been shown using three real life data sets. The MOEGT‐II distribution has been demonstrated as better fit than Exponentiated Gumbel Type‐II (EGT‐II), Marshall–Olkin Gumbel Type‐II (MOGT‐II), Gumbel Type‐II (GT‐II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions.
Highlights
Probability distributions are mostly used in survival analysis for modeling data because it provides insight interest in the nature of various parameters and functions mainly in the failure rate function. e lifetime distributions are used in reliability engineering and life data analysis
The exponential distribution has been modified by many researchers; for example, Gupta and Kundu [5, 6] defined new families of exponential distribution; exponentiated generalized class of distributions was introduced by Cordeiro et al [7]; and Exponentiated Generalized Gumbel distribution was proposed by Andrade et al [8]
Special cases of this family were discussed by using Exponential, Weibull, Gamma, and Log Normal distribution. e survival function of a two parametric exponential distribution was obtained by using the survival function of one-parametric exponential distribution
Summary
Probability distributions are mostly used in survival analysis for modeling data because it provides insight interest in the nature of various parameters and functions mainly in the failure rate function. e lifetime distributions are used in reliability engineering and life data analysis. Al-Saiari et al [17] introduced a new three-parameter distribution named as Marshall–Olkin Extended Burr Type XII Distribution.A four-parameter distribution named as a Marshall–Olkin Exponential Weibull (MOEW) distribution for skewed positive data was proposed by Pogany et al [18]. Gillariose et al [23] introduced a new Marshall–Olkin Modified Lindley Distribution; Marshall Olkin Power Lomax distribution was proposed by Haq et al [24]; Ogunde et al [25] proposed the Extended Gumbel Type-II distribution; and Almetwally et al [26] derived various properties of Marshall–Olkin Alpha Power Weibull distribution. We derive a new probability distribution by employing the cdf and pdf of Gumbel type-II in the Marshall–Olkin family of distributions called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) distribution.
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