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On a New Shot Noise Process and the Induced Survival Model

Title
On a New Shot Noise Process and the Induced Survival Model
Authors
Cha J.H.Finkelstein M.
Ewha Authors
차지환
SCOPUS Author ID
차지환scopus
Issue Date
2017
Journal Title
Methodology and Computing in Applied Probability
ISSN
1387-5841JCR Link
Citation
pp. 1 - 21
Keywords
Failure rateGeneralized Polya processHistory-dependent residual lifetimePoisson processShot noise process
Publisher
Springer New York LLC
Indexed
SCIE; SCOPUS scopus
Abstract
Traditionally, in applications, the shot noise processes have been studied under the assumption that the underlying arrival point process (shock process) is the homogeneous (or nonhomogeneous) Poisson process. However, most of the real life shock processes do not possess the independent increments property and the Poisson assumption is made just for simplicity. Recently, in the literature, a new point process, the generalized Polya process (GPP), has been proposed and characterized. The GPP is defined via the stochastic intensity that depends on the number of events in the previous interval and, therefore, does not possess the independent increments property. In this paper, we consider the GPP as an underlying shock process for the shot noise process. The corresponding survival model is considered and the survival probability and its failure rate are derived and thoroughly analyzed. Furthermore, a new concept, the history-dependent residual life time, is defined and discussed. © 2017 Springer Science+Business Media New York
DOI
10.1007/s11009-017-9550-y
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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