Convolutions of erlang and of Pascal distributions with applications to reliability

• Autorzy: Jasiulewicz H. , Kordecki W.
• Języki publikacji: EN

Abstrakty

EN

The main aim of the paper is to give a generalization of the results given by Sen and Balakrishnan in [7]. The results obtained are used to calculate the reliability of some class of systems.

Słowa kluczowe

EN

Pascal distribution; Bernoulli scheme; reliability problem

PL

schemat Bernoulliego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 1
• Strony: 231--238
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Jasiulewicz H.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław

autor

Kordecki W.

• Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław

Bibliografia

• [1] N. L. Johnson, S. Kotz (1969), Discrete Distributions, Wiley, New York.
• [2] N. L. Johnson, S. Kotz, N. Balakrishnan (1994), Continuous Univariate Distributions - 1, Wiley, New York.
• [3] W. Kordecki (1997), Reliability bounds for multistage structures with independent components, Stat. Probab. Lett. 34, pp. 43-51.
• [4] M. V. Lomonosov (1974), Bernoulli scheme with closure, Problems Inform. Transmission 10, pp. 73-81.
• [5] A. M. Mathai, (1982), Storage capacity of a dam with gamma type inputs, Ann. Inst. Statist. Math. 34, pp. 591-597.
• [6] S. M. Ross (1993), Introduction to Probability Models, 5th ed. Academic Press, New York.
• [7] A. Sen, N. Balakrishnan (1999), Convolution of geometries and a reliability problem, Stat. Probab. Lett. 43, pp. 421-426.