On Properties of the Phase-type Mixed Poisson Process and its Applications to Reliability Shock Modeling

Although Poisson processes are widely used in various applications for modeling of recurrent point events, there exist obvious limitations. Several specific mixed Poisson processes (which are formally not Poisson processes any more) that were recently introduced in the literature overcome some of th...

Full description

Saved in:
Bibliographic Details
Published inMethodology and computing in applied probability Vol. 24; no. 4; pp. 2933 - 2960
Main Authors Goyal, Dheeraj, Hazra, Nil Kamal, Finkelstein, Maxim
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2022
Springer Nature B.V
Subjects
Business and Management
Economics
Electrical Engineering
Failure rates
Life Sciences
Markov analysis
Mathematics and Statistics
Modelling
Poisson density functions
Statistics
60E15
Shock models
Mixed Poisson process
Phase-type distribution
Non-homogeneous Poisson process
60K10
Online AccessGet full text

Cover

More Information
Summary:Although Poisson processes are widely used in various applications for modeling of recurrent point events, there exist obvious limitations. Several specific mixed Poisson processes (which are formally not Poisson processes any more) that were recently introduced in the literature overcome some of these limitations. In this paper, we define a general mixed Poisson process with the phase-type (PH) distribution as the mixing one. As the PH distribution is dense in the set of lifetime distributions, the new process can be used to approximate any mixed Poisson process. We study some basic stochastic properties of the new process and discuss relevant applications by considering the extreme shock model, the stochastic failure rate model and the δ -shock model.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-022-09961-2