The Kumaraswamy-geometric distribution

Abstract

In this paper, the Kumaraswamy-geometric distribution, which is a member of the T-geometric family of discrete distributions is defined and studied. Some properties of the distribution such as moments, probability generating function, hazard and quantile functions are studied. The method of maximum likelihood estimation is proposed for estimating the model parameters. Two real data sets are used to illustrate the applications of the Kumaraswamy-geometric distribution.

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

“…(21). Akinsete et al (2014) also proved that this distribution can also be derived by considering log-Kumararswamy distribution instead of Kuamarswamy distribution and taking W(x) = − log(1 − x).…”

“…(19) when W(x) = − log(1 − x). Akinsete et al (2014) considered T as the Kumaraswamy (1980) distribution with cdf…”

The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

“…The method of generalization of distributions by the Kumaraswamy-G generator proposed by [1] is one of the preferable techniques in distribution theory and was considered by many authors in recent years. For instance, the Kumaraswamy-Weibull distribution [2], Kumaraswamy binomial [3], Kumaraswamy generalized gamma [4], Kumaraswamy-Gumbel [5], Kumaraswamy generalized half-normal [6], Kumaraswamy log-logistic [7], Kumaraswamy-Birnbaum-Saunders [8], Kumaraswamy inverse Weibull [9], Kumaraswamy double inverse exponential [10], Kumaraswamy power series [11], Kumaraswamy-Pareto [12], Kumaraswamy generalized linear failure rate [13], Kumaraswamy exponentiated Pareto [14], Kumaraswamy quasi-Lindley [15], Kumaraswamy generalized Pareto [16], Kumaraswamy-Burr XII distribution [17], Kumaraswamy generalized exponentiated Pareto [18], Kumaraswamy generalized Lomax [19], Kumaraswamy geometric [20], Kumaraswamy half-Cauchy distrbution [21], Kumaraswamy generalized Rayleigh [22], Kumaraswamy-Dagum distribution [23], Kumaraswamy inverse Rayleigh [24], Kumaraswamy inverse exponential [25], Kumaraswamy -Kumaraswamy [26], Kumaraswamy transmuted exponentiated modified Weibull [27], Kumaraswamy odd loglogistic [28], Kumaraswamy skew-normal [29].…”

Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions

“…Using (8), a number of modifications of the existing distributions have been proposed in the literature. A brief list of these modifications is presented in Table 3: Eugene et al (2002) introduced the beta generated method that uses the beta distribution with parameters a and b as the generator to develop the beta generated distributions.…”