A Resilience Parameter Model Generated by a Compound Distribution

Abstract

In this paper, we shall attempt to extend the generalized exponential geometric distribution of Silva et al.[1]. The new four-parameter distribution also generalizes the Weibull-geometric distribution of Barreto-Souza et al. [2], exponentiated Weibull, and several other lifetime distributions as special cases. A useful characteristic of the new distribution is that its failure rate function can have different shapes. We first study certain basic distributional properties of the new distribution and provide closed form expressions for its moment generating function and moments. General expressions are also obtained for the order statistics densities and stress-strength parameter. Our findings happen to enfold several known results as special cases. The model parameters are estimated by the maximum likelihood method and the Fisher information matrix is discussed. Finally, the model is applied to a real data set and its advantage over some rival models is illustrated.