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 \(S_{k} =\sum_{t=1}^{T_{k}}Y_{t}\).
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Koutras, M.V., Eryilmaz, S. Compound Geometric Distribution of Order k . Methodol Comput Appl Probab 19, 377–393 (2017). https://doi.org/10.1007/s11009-016-9482-y
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DOI: https://doi.org/10.1007/s11009-016-9482-y