# Compound Geometric Distribution of Order k

*Markos V. Koutras* () and
*Serkan Eryilmaz* ()

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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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**Persistent link:** https://EconPapers.repec.org/RePEc:spr:metcap:v:19:y:2017:i:2:d:10.1007_s11009-016-9482-y

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**DOI:** 10.1007/s11009-016-9482-y

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