A New Versatile Discrete Distribution for Censored Data: Frequentist and Bayesian Methods With Real-Life Applications

This study introduces a novel and highly flexible class of discrete probability distributions tailored to model the diverse monotonic failure-rate patterns frequently observed in stock-market data. The proposed distribution accommodates outliers effectively and serves as a discrete analogue of the exponential law, enabling analysts to derive robust and interpretable insights into market dynamics. Fundamental mathematical characteristics of the distribution—such as the probability-generating function, mean, and variance—are thoroughly derived. The model is further extended to handle Type-II censored data, enhancing its applicability to real-world scenarios where incomplete observations are common. Parameter estimation is performed using both maximum-likelihood and Bayesian approaches, with a special focus on techniques suitable for censored samples. The performance and reliability of the estimators are examined through extensive simulation studies. To validate the practical utility of the model, it is applied to five real stock-market datasets obtained from Indiastat. The results demonstrate a superior empirical fit, affirming the model’s relevance in capturing the underlying patterns of financial time series. This distribution provides a valuable tool for analysts and researchers in the fields of financial statistics, risk modeling, and market behavior analysis.