Please use this identifier to cite or link to this item:
Title: On Some Issues Of Stochastic Comparisons & Their Applications
Authors: Panja, Arindam
Keywords: Stochastic order
Order statistics
Redundancy allocation
Claim amounts
Issue Date: 2023
Publisher: Indian Statistical Institute, Kolkata
Citation: 183p.
Series/Report no.: ISI Ph. D Thesis;TH590
Abstract: One of the important objectives of statistics is the comparison of random quantities. These comparisons are mainly based on the comparison of some measures associated with these random quantities. For example, it is very common to compare two random variables in terms of their means, medians, or variances. In some situations, comparisons based only on two single measures are not very informative. The necessity of providing more detailed comparisons of two random quantities has motivated the development of the theory of stochastic orders, which has grown significantly during the last 50 years. Stochastic order refers to comparing two random quantities in some stochastic sense. It is an important tool used in many diverse areas of statistics, reliability, economics, etc. Reliability theory and actuarial science are two most important areas where stochastic orders are studied extensively. Usual stochastic ordering, hazard rate ordering, reversed hazard rate ordering for lifetimes of series and parallel systems with heterogeneous and dependent componentshave beenestablished. Dispersive and star order for one heterogeneous and one homogeneous dependent series or parallel systems havealso been established. For two finite mixture models’ comparison, results have beenestablished under the usual stochastic order, hazard rate order and reversed hazard rate order. Various up and down-shifted ordering results have beenestablished for two important continuous mixture models: Frailty and Resilience. Data analysis has been done for illustration purposes. To find the optimal set of redundant components or systems, the usual stochastic ordering, hazard rate ordering and reversed hazard rate ordering of systems lifetimes under active redundancy allocation have beenestablished. Data analysis has also been donein this contextfor illustration purposes. Actuarial science is another area where stochastic ordershave extensivepotential for application. Usual stochastic ordering and star ordering results have beenestablished for the largest and aggregate claim amounts of two heterogeneous portfolios. Numerical exampleshave been provided in this context to illustrate the results thus obtained.
Description: This thesis is under the supervision of Prof. Biswabrata Pradhan
Appears in Collections:Theses

Files in This Item:
File Description SizeFormat 
Thesis_Arindam panza-9-10-23.pdfThesis8.28 MBAdobe PDFView/Open
Form 17_Arindam Panja.pdfForm-17125.78 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.