# Compound Geometric Distribution of Order k

Markos V. Koutras () and Serkan Eryilmaz ()
Markos V. Koutras: University of Piraeus
Serkan Eryilmaz: Atilim University

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 2, 377-393

Abstract: 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,… 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 S k = ∑ t = 1 T k Y t $S_{k} =\sum_{t=1}^{T_{k}}Y_{t}$ .

Keywords: Compound distributions; Geometric distribution of order k; Phase-type distribution; Runs; 60E05; 60G40; 60G50; 60J10 (search for similar items in EconPapers)
Date: 2017
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