Power series expansions for the probability distribution, mean value and variance functions of a geometric process with gamma interarrival times

PEKALP M. H., AYDOĞDU H.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.388, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 388
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1016/j.cam.2020.113287
  • Dergi Adı: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: Geometric process, Power series expansion, Geometric function, Variance function, Gamma distribution, QUASI-RENEWAL PROCESS, 2ND MOMENT FUNCTION, INTEGRAL-EQUATION
  • Ankara Üniversitesi Adresli: Evet

Özet

The geometric process is used widely as a stochastic monotone model in many areas since its introduction. In this study, this process is considered when the distribution of the first interarrival time follows a gamma distribution. One dimensional probability distribution of the process is obtained by expanding the convolution of gamma distributions into a power series. Further, its mean value, second moment and variance functions are derived as a power series expansion with the help of the integral equations given for mean value and second moment functions. The illustrative examples are also given. Finally, a real-world data set is considered to see the applicability of the results. (C) 2020 Elsevier B.V. All rights reserved.