Marshall–Olkin Extended Gumbel Type-II Distribution: Properties and Applications

Author:

Willayat Farwa1,Saud Naz2,Ijaz Muhammad3ORCID,Silvianita Anita4,El-Morshedy Mahmoud56ORCID

Affiliation:

1. Department of Statistics, Gulab Devi Educational Complex, Lahore, Pakistan

2. Department of Statistics, Lahore College for Women University, Lahore, Pakistan

3. Department of Mathematics and Statistics, University of Haripur, Haripur, Pakistan

4. School of communications and business, Telkom University, Jalan Terusan Buah Batu 1, Bandung 40257, Indonesia

5. Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

6. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

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.

Publisher

Hindawi Limited

Subject

Multidisciplinary,General Computer Science

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