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Abstract
Length-biased sampling has been observed to arise in many biomedical applications such as family history and disease, early detection of disease, survival and intermediate events, and in the study of the latency period of AIDS among patients who received blood transfusions. Recently there has been an increased interest in discrete distributions of order k which are more flexible than their ordinary counterparts when k = 1. In this paper we develop factorial moment distributions of some well known discrete distributions and length-biased versions of some of the distributions of order k and investigate their properties. Their relationship to the corresponding length-biased distributions in the ordinary case is investigated.
