On the exact distribution and mean value function of a geometric process with exponential interarrival times

AYDOĞDU H., KARABULUT İ., Sen E.

STATISTICS & PROBABILITY LETTERS, vol.83, no.11, pp.2577-2582, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 83 Issue: 11
  • Publication Date: 2013
  • Doi Number: 10.1016/j.spl.2013.08.003
  • Journal Name: STATISTICS & PROBABILITY LETTERS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2577-2582
  • Keywords: Exponential distribution, Geometric renewal function, Power series, Weibull distribution
  • Ankara University Affiliated: Yes

Abstract

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power series expansion is derived for the geometric renewal function by using an integral equation and evaluated in a computational perspective. Further, an extension is provided for the power series expansion of the geometric renewal function in the case of the Weibull distribution. (C) 2013 Elsevier B.V. All rights reserved.