A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference

This study introduces a unique flexible family of discrete probability distributions for modeling extreme count and zero-inflated data with different failure rates. Certain significant mathematical properties, such as the cumulant generating function, moment dispersion index, L-moments, ordinary moments, central are derived. The new rate function offers wide range flexibility, including “upside down”, “monotonically decreasing”, “bathtub”, increasing” “decreasing-constant rate” “constant”. Moreover, mass accommodates many useful shapes “right skewed no peak”, “symmetric”, one peak” “left peak”. To obtain characterization findings, hazard conditional expectation certain random variable both employed. Both Bayesian non-Bayesian estimate methodologies considered when estimating, assessing, comparing inferential efficacy. estimation approach squared error loss is suggested, it explained. Markov chain Monte Carlo simulation studies performed using Metropolis Hastings algorithm Gibbs sampler to compare vs. results. Four real-world applications sets used evaluate versus techniques. more real illustrate significance versatility class.