Abstract
In this article, we introduce a new flexible discrete family of distributions, which accommodates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets.
Highlights
The Marshall–Olkin family of distributions was introduced by [1]
We study a special case of this family, namely, discrete Weibull Marshall–Olkin exponential (DWMOE) distribution
We proposed a new discrete Weibull Marshall–Olkin family of distributions with two shape parameters
Summary
The Marshall–Olkin family of distributions was introduced by [1] This is an interesting endeavour for associating additional parameter to an existing baseline. Some discrete distributions derived based on popular continuous models, for example, see, refs. The proposed new discrete model has positively skewed, decreasing and symmetric probability mass function (pmf). We offered a comparison of the estimation methods and real-life data application to explain how well the proposed model give consistently better fit than the other well-known discrete distributions. The rest of the paper is outlined as follows: In Section 2, we propose a new discrete family of distributions and a special case of the derived family together with its probabilistic properties.
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