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

Due to the advance computer technology, use of probability distributions has been raised up solve real life problems. These applications are found in reliability engineering, sciences, economics, psychology, survival analysis, and some others. This study offers a new model called Marshall–Olkin Extended Gumbel Type-II (MOEGT-II) which can various shapes failure rate function. The proposed distribution is capable increasing, decreasing, reverse J-shaped, upside down bathtub Various statistical properties derived such as alternate expressions for density function, special cases MOEGT-II distribution, quantile Lorenz curve, Bonferroni curve. Estimation unknown parameters carried out by method maximum likelihood. A simulation conducted using three different iterative methods with samples sizes n. usefulness potentiality have shown data sets. demonstrated better fit than Exponentiated (EGT-II), (MOGT-II), (GT-II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), Kumaraswamy (KIW) distributions.