Properties, Estimations and Applications of new Families of Continuous Distributions

Abstract

This thesis primarily aims at the advances towards the literature of probability distributions. With the emergence of big data movement supported by the increased availability of sensors and data acquisition systems, the researchers are bound to confront with complex data structures of unprecedented nature. The need of developing more, competent, comprehensive, parsimonious, flexible and efficient probabilistic schemes is unavoidable in given data-rich environment. Our research is mainly motivated by the aforementioned requirements and presents new families of distributions capable of mapping complex real phenomena originated from multidisciplinary research fields. The advances are made by amending well known existing methodologies of generating novel families of distributions, such as T-X family, Transmutation approach, unit interval method and Logarithmic transformation scheme. As outcome of this thesis, we firstly develop three new families of distributions, named Exponential negative binomial-X family, Logistic-X family and modified generalized Marshal and Olkin family. These new families of distributions are demonstrated as a capable candidate of modeling symmetric as well as skewed (right) data with noticeable flexibility and efficiency. Further proceedings of this thesis document the introduction of the new cubic transmuted-G family capable of handling various forms of hazard functions. Moreover, we also provide a novel alternative to the famous existing cubic rank transmutation along the lines. The scope of this thesis is further widened by focusing on, yet, another approach of devising new classes of distributions namely unit interval method. As the result of intuitive exploitation of the existing technique, we provide new unit Weibull family of distributions. The new family is elaborated in competitive environment. Lastly, ix we introduce log-expo transformation family by using logarithmic transformation. The legitimacy of the developments reported in this thesis is demonstrated on mathematical front, the results of which are then verified through rigorous simulation studies. Furthermore, the notion of generality is maintained by pursuing the proposed models under classic approach as well as with respect to Bayesian framework. Moreover, to meet the requirement of practicality, various types of censoring schemes, such as Type-I censoring, Type-II censoring and random censoring are also considered. The applicability of the newly proposed schemes is elaborated by using various data sets, well cherished in multidisciplinary research literature. The comparative performance of newly developed procedures is discussed in details throughout the thesis. The inspiring extent of gain associated with our propositions in comparison to contemporary models is noticeable.