Some Properties on Fréchet-Weibull Distribution with Application to Real Life Data

Research, development and extensive use of generalized form of distributions in order to analyze and modeling of applied sciences research data has been growing tremendously. Weibull and Frechet distribution are widely discussed for reliability and survival analysis using experimental data from physical, chemical, environmental and engineering sciences. Both the distributions are applicable to extreme value theory as well as small and large data sets. Recently researchers develop several probability distributions to model experimental data as these parent models are not adequate to fit in some experiments. Modified forms of the Weibull distribution and Frechet distribution are more flexible distributions for modeling experimental data. This article aims to introduce a generalize form of Weibull distribution known as Frechet-Weibull Distribution (FWD) by using the T-X family which extends a more flexible distribution for modeling experimental data. Here the pdf and cdf with survival function [S(t)], hazard rate function [h(t)] and asymptotic behaviour of pdf and survival function and the possible shapes of pdf, cdf, S(t) and h(t) of FWD have been studied and the parameters are estimated using maximum livelihood method (MLM). Some statistical properties of FWD such as mode, moments, skewness, kurtosis, variation, quantile function, moment generating function, characteristic function and entropies are investigated. Finally the FWD has been applied to two sets of observations from mechanical engineering and shows the superiority of FWD over other related distributions. This study will provide a useful tool to analyze and modeling of datasets in Mechanical Engineering sciences and other related field.