On Cumulative Information Measures: Properties, Inference and Applications

Date of Submission

October 2023

Date of Award

10-1-2024

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Operations Research

Department

SQC and OR Unit (Kolkata)

Supervisor

Pradhan, Biswabrata (SQCOR-Kolkata; ISI)

Abstract (Summary of the Work)

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.

Comments

ProQuest Collection ID: https://www.proquest.com/pqdtlocal1010185/dissertations/fromDatabasesLayer?accountid=27563

Control Number

ISILib-TH

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/2146

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