c(θ)-Geometric Distribution of Order k and Some of its Properties

Observe that (1.1) yields equation (1.2) if we take y = x − 1, hence equation (1.2) is a transformation of equation (1.1). The random variable X in equation (1.1) and the random Y in equation (1.2) are often described as; the number of independent (Bernoulli’s) trials on which the first success occurs and the number of failures before the first success occurs. G ABSTRACT In this research work, we present a new distribution function that modifies and generalize the classical geometric distribution of order k via c(θ)-geometric distribution which we called the c(θ)-geometric distribution of order k (simply θ-geometric distribution of order k if θ ≥ 0 and reverse θ-geometric distribution of order k if θ < 0.) for every θ ∈ Z. The associated cumulative distribution, generating functions and statistics were also established. The results obtained in this paper improve, generalize and complement the works of several authors in the literature. Original Research Article