Discrete Additive Weibull Geometric Distribution

Abstract

Discretizing a continuous distribution has received much attention among researchers recently. Discrete analogue of the well-known continuous distributions such as Normal, Exponential, Weibull, Laplace, Rayleigh, and so on, are available in the literature. In this paper, we introduce a discrete version of the additive Weibull geometric distribution of Elbatal et al. [1]. Discrete Weibull, discrete modified Weibull, discrete Weibull geometric, discrete exponential geometric, discrete Rayleigh distribution, and so on, are sub models of this distribution. We study some properties of the new distribution. The hazard rate function of the new distribution is monotonically increasing or decreasing or bathtub shape based on the values of the shape parameters. The method of maximum likelihood estimation is used for estimating the model parameters. A simulation study is carried out to show the performance of the maximum likelihood estimate of parameters of the new distribution. An application of this distribution to a real data set is also presented.

Keywords

• Additive Weibull distribution
• discrete Weibull distribution
• geometric distribution
• hazard rate function
• order statistics
• Weibull distribution