Compound Geometric Distribution of Order <i>k</I>

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Date

2017

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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

The distribution of the number of trials until the first k consecutive successes in a sequence of Bernoulli trials with success probability p is known as geometric distribution of order k. Let T (k) be a random variable that follows a geometric distribution of order k, and Y (1),Y (2),aEuro broken vertical bar a sequence of independent and identically distributed discrete random variables which are independent of T (k) . In the present article we develop some results on the distribution of the compound random variable Y-t.

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Koutras, Markos/0000-0001-5160-2405; Eryilmaz, Serkan/0000-0002-2108-1781
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Koutras, Markos ORCID logo
Eryilmaz, Serkan ORCID logo

Keywords

Compound distributions, Geometric distribution of order k, Phase-type distribution, Runs

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Q4

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Q3

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Volume

19

Issue

2

Start Page

377

End Page

393

URI

https://doi.org/10.1007/s11009-016-9482-y
 https://hdl.handle.net/20.500.14411/2868

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