The distributions of sum, minima and maxima of generalized geometric random variables

TANK F., Eryilmaz S.

STATISTICAL PAPERS, cilt.56, sa.4, ss.1191-1203, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 56 Sayı: 4
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s00362-014-0632-4
  • Dergi Adı: STATISTICAL PAPERS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1191-1203
  • Anahtar Kelimeler: Geometric distribution of order k, Phase-type distribution, Reliability, FIBONACCI-TYPE POLYNOMIALS, ORDER-K, BERNOULLI TRIALS, SUCCESS, STRINGS, STATISTICS, SEQUENCES
  • Ankara Üniversitesi Adresli: Evet

Özet

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.