Zero-one inflated negative binomial - beta exponential distribution for count data with many zeros and ones

The characteristic of count data that have a high frequency of zeros and ones can be considered under a zero-one inflated distribution. In this article, we present a zero-one inflated negative binomial - beta exponential distribution to analyze for such data. This distribution shows that it is extended the mixture negative binomial with beta exponential distributions, was proposed by Pudprommarat, Bodhisuwan, and Zeephongsekul (2012). Some important properties of this distribution are discussed, which include probability mass function, moment generating function, moment about the origin, mean and variance. Additionally, some sub-models are presented. Its parameters are also derived based on the maximum likelihood estimation procedure. The applicability of the proposed distribution is demonstrated for fitting to three real data sets. We also evaluate the abilities of model selection relying on the negative log-likelihood, Akaike information criterion, mean absolute error, root mean squared error, discrete Kolmogorov–Smirnov test and Anderson-Darling tests. Results from this study indicate the zero-one inflated negative binomial - beta exponential distribution has shown the best fit for these data sets when it is compared with some sub-models and the zero-one inflated of traditional distributions.