On Cumulative Information Measures: Properties, Inference and Applications

Abstract

In this thesis, various weighted information measures based on cumulative distribution functions and survival functions of the underlying random variables are proposed and their properties are studied. Dynamic information measures are introduced which are defined in terms of the residual and past lifetimes of the underlying random variables. Aging classes based on the dynamic information measures are discussed and characterization results for Rayleigh and power distributions are obtained. Non-parametric estimators of these measures are proposed using empirical distribution function, L-Statistics and Kernel function. Asymptotic properties of these estimators are investigated. Exponentiality tests for complete and censored data and uniformity tests are developed as applications. Also Applications of cumulative residual extropy measure in reliability engineering and hypothesis testing problems are discussed. Optimal designs for progressive Type-II censored experiments using cumulative entropy measures are investigated. Numerous examples are provided throughout the course of this thesis for illustrations.