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The beta Weibull Poisson distribution. (English) Zbl 1449.60019

Summary: Providing a wider distribution is always precious for statisticians. A new five-parameter distribution called the beta Weibull Poisson is proposed, which is obtained by compounding the Weibull Poisson and beta distributions. It generalizes several known lifetime models. We obtain some properties of the proposed distribution such as the survival and hazard rate functions, quantile function, ordinary and incomplete moments, order statistics and Rényi entropy. Estimation by maximum likelihood and inference for large samples are addressed. The potentiality of the new model is shown by means of a real data set. In fact, the proposed model can produce better fits than some well-known distributions.

MSC:

60E05 Probability distributions: general theory
62P99 Applications of statistics
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