Fréchet Family Of Distributions And Its Applications

The use of classical distributions to model data spans many disciplines and dates back many years.The following are some of these disciplines:actuarial science,economics,insurance,finance,medicine,engineering,biology,demography,and ecology.However flexible distributions are always required to describe,clarify,and make predictions about the actual events that are the subject of such research.To develop new families of distributions that are either simpler to use or better reflect specific real-world situations,academics have experimented with a variety of methods.In this regard,a number of well-known generators are developed among which Transformed-Transformer(T-X)is worth appreciating and mentioning.But matter of fact it lacks the construction of bounded domain T-X phenomenon.Therefore,we are going to unveil a new T-X bounded family of distributions for univariate,bivariate and multivariate cases,by combining the Frechet and log-logistic,Burr-Ⅲ and log-logistic,Burr-X and log-logistic and Burr-XII and log-logistic.This dissertation contains four essays;all these essays’central idea is to focus on T-X families in univariate,bivariate and multivariate cases along with applications.In the first essay,we developed and studied the upper bounded domain Frechet and log-logistic distribution(UFLD)with various properties,entropy measures and characterization of the proposed function along real lifetime data applications in an elegant manner.The second essay deals with the lower bounded domain Frechet and log-logistic distribution(LFLD).Its various properties including entropy measure and characterization via the entropy principle are discussed.A simulation study for parameter estimation via a method of moments(MM),L-moments(L-M)and maximum likelihood estimation(MLE)is presented.Moreover,flood data application by using four data sets is also presented.The third essay explores bivariate T-X copula construction,Archimedean copulas and Farli-Gumbel-Morgenstern(F-G-M)copula for the construction of upper bounded bivariate Frechet log-logistic distribution(BUBFLD).Various properties and applications of the BUBFLD are also discussed in this essay.The fourth essay investigates the multivariate lower bounded domain function along with various properties and applications.