The modeling of count data and their applications have garnered significant attention in various research domains, particularly in studies involving uncertainty, risk analysis, and decision-making processes. In this paper, we present a novel discrete inverse exponentiated Pareto distribution that is developed using the discretization of survival function technique. The resulting distribution exhibits many desirable characteristics, thus rendering it ideal for analyzing discrete data characterized by heavy tails and positive skewness. The risk function has the flexibility to assume monotonically decreasing and upside-down bathtub shapes. Statistical properties, such as moments, entropy, quantile function, stress-strength reliability, and probability generating function, are discussed in this article. The validity of the suggested distribution was verified by conducting Monte Carlo simulations whereby Bayesian estimation technique using squared error loss function with informative prior always performed better than the maximum likelihood estimation technique, reducing the mean squared errors by up to 15–40% for samples of size n = 15–120. The desired distribution generated the least Akaike information criterion (346.01267) and highest chi-square p-value (0.78845) among six competing distributions for the analysis of rat kidney lesions. For UK coal mining strike data, new model gave the smallest Akaike information criterion (379.58014) and chi-square statistics (2.00388). To demonstrate the practical utility of the proposed distribution, it is applied to two real count datasets. The first dataset contains observations on corticosteroid-induced kidney lesions in rat embryos, representing a toxicological application relevant to radiation research and health-related risk analysis. The second dataset records the number of strike outbreaks in the UK coal mining industry over a period of one decade, illustrating its usefulness in industrial risk modeling and labor economics. The findings highlight the practical utility of discrete inverse exponentiated Pareto distribution in radiation-related toxicology, labor economics, and industrial manufacturing, accurately reflecting its scope in modeling specialized count datasets. quantitatively, it is evident that suggested model is an excellent model for right skewed count data.
Hassan et al. (Tue,) studied this question.