A discrete analogue of odd Lomax generator of distributions for extreme and zero-inflated count data under various shapes of failure rates: Theory and inference

Abstract

In this article, we introduce a discrete analogue of odd Lomax generator of distributions. The new discrete class can be utilized as a probabilistic tool to generalize any discrete baseline model. After proposing the new class, two special discrete models are investigated and discussed in detail. Some mathematical and statistical properties including, probability mass function, hazard rate function, quantile, crude moments, index of dispersion, entropies, order statistics, and L-moment statistics, are derived. It is found that the presented discrete class can be used to model symmetric and asymmetric data under different types of kurtosis shapes. It can be utilized to explain and analyze overdispersion data with extreme, zero-inflated or outliers' observations. Furthermore, it can be used to discuss various shapes of hazard rates including monotone increasing, monotone decreasing, unimodal, bathtub, unimodal-bathtub, among others. We discuss the estimation of the class parameters by the maximum likelihood approach. The performance of the estimation method is tested via MCMC simulation technique. Finally, to demonstrate the proposed methodology in a real-life scenario, three real data sets are considered to show the applicability of the proposed generator.