A geometric process with Hjorth marginal: Estimation, discrimination, and reliability data modeling

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Tarih

2022

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Wiley

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

The geometric process is one of the important simple monotonic processes with a positive ratio parameter in the theory of stochastic processes. Simply, it can be thought of as a generalization of the renewal process (RP). In the current paper, we mainly study the geometric process with the Hjorth marginal distribution, with parameters theta and lambda, for being able to model the successive inter-arrival times with a trend. We first examine inference problem for the mentioned process from different perspectives and obtain the different estimators of its parameters by employing different estimation methods such as maximum likelihood, modified moments, modified maximum spacing, and modified least-squares. The efficiencies of these estimators are compared via a series of extensive simulation studies in the paper. Further, we give also a discrimination statistic for discriminating among geometric processes with the Hjorth distribution and its alternatives. This is quite important to select the optimal geometric process model for data. Finally, a modeling study by using the geometric process with the Hjorth distribution is provided in detail to display its effectiveness to model the reliability data sets.

Açıklama

Anahtar Kelimeler

discrimination; estimation; geometric processes; inter-arrival times; marginal distributions

Kaynak

Quality and Reliability Engineering International

WoS Q Değeri

Q3

Scopus Q Değeri

Q2

Cilt

38

Sayı

5

Künye