Abstract
An exponentiated Weibull-geometric distribution is defined and studied. A new count data regression model, based on the exponentiated Weibull-geometric distribution, is also defined. The regression model can be applied to fit an underdispersed or an over-dispersed count data. The exponentiated Weibull-geometric regression model is fitted to two numerical data sets. The new model provided a better fit than the fit from its competitors.
Highlights
Many techniques for generating families of discrete distributions have been developed in the literature
The ranked probability score (RPS) is defined by Weigel et al (2006) as a statistic that measures the discrepancy between the theoretical cumulative distribution function (CDF) and empirical CDF
We apply the generalized Poisson regression (GPR) model defined by Famoye (1993), the exponentiated exponential geometric regression (EEGR) model defined by Famoye and Lee (2017) and the exponentiated Weibull-geometric regression (EWGR) model to two count data sets
Summary
Many techniques for generating families of discrete distributions have been developed in the literature. Nekoukhou and Bidram (2015) gave a long list of these works Another method to generalize an existing distribution is by adding parameters to the distribution to form an exponentiated family (Lee et al, 2013 and the references therein). We define an exponentiated Weibull-geometric distribution by using the T-R framework proposed by Alzaatreh et al (2013) and recently used by Hamed et al (2018) This new distribution is a discrete distribution and it is the discrete analogue of the continuous exponentiated Weibull distribution. EEGD with one shape parameter provided excellent fits to many count data sets This observation motivated the definition and study of EWGD.
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