The Distributions of Sum, Minima and Maxima of Generalized Geometric Random Variables

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2015

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Springer

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Industrial Engineering
(1998)
Industrial Engineering is a field of engineering that develops and applies methods and techniques to design, implement, develop and improve systems comprising of humans, materials, machines, energy and funding. Our department was founded in 1998, and since then, has graduated hundreds of individuals who may compete nationally and internationally into professional life. Accredited by MÜDEK in 2014, our student-centered education continues. In addition to acquiring the knowledge necessary for every Industrial engineer, our students are able to gain professional experience in their desired fields of expertise with a wide array of elective courses, such as E-commerce and ERP, Reliability, Tabulation, or Industrial Engineering Applications in the Energy Sector. With dissertation projects fictionalized on solving real problems at real companies, our students gain experience in the sector, and a wide network of contacts. Our education is supported with ERASMUS programs. With the scientific studies of our competent academic staff published in internationally-renowned magazines, our department ranks with the bests among other universities. IESC, one of the most active student networks at our university, continues to organize extensive, and productive events every year.

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Abstract

Geometric distribution of order as one of the generalization of well known geometric distribution is the distribution of the number of trials until the first consecutive successes in Bernoulli trials with success probability . In this paper, it is shown that this generalized distribution can be represented as a discrete phase-type distribution. Using this representation along with closure properties of phase-type distributions, the distributions of sum, minima and maxima of two independent random variables having geometric distribution of order are obtained. Numerical results are presented to illustrate the computational details.

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tank, fatih/0000-0003-3758-396X; Tank, Fatih/0000-0003-3758-396X; Eryilmaz, Serkan/0000-0002-2108-1781
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tank, fatih ORCID logo
Tank, Fatih ORCID logo
Eryilmaz, Serkan ORCID logo

Keywords

Geometric distribution of order k, Phase-type distribution, Reliability

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Volume

56

Issue

4

Start Page

1191

End Page

1203

URI

https://doi.org/10.1007/s00362-014-0632-4
 https://hdl.handle.net/20.500.14411/791

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