Asian Journal of Probability and Statistics

This study introduces the Discrete New Generalized Weibull Distribution (DNGWD), a flexible discrete lifetime model intended for count data in reliability engineering, actuarial science, and risk analysis. The distribution is obtained as a discrete analogue of the new generalized Weibull distribution. Its principal statistical properties are derived, including non-central moments, skewness, kurtosis, the coefficient of variation, the index of dispersion, generating functions, survival and hazard-rate functions, entropy, and order statistics. The index of dispersion demonstrates that the model can accommodate both overdispersion and under dispersion under different parameter settings, while the hazard-rate function can assume increasing, decreasing, constant, and bathtub-shaped forms. Model parameters are estimated using maximum likelihood and Bayesian methods. Bayesian estimators are developed under the squared error loss function and the Weibull linear exponential loss function, together with credible intervals. A Markov chain Monte Carlo simulation study evaluates estimator performance across selected parameter values and sample sizes using bias, variance, mean squared error, coverage probability, and credible intervals. The practical applicability of the model is examined using count data on stocks reaching the upper circuit limit on the National Stock Exchange of India. Goodness-of-fit comparisons with the discrete Burr, binomial, Poisson, discrete exponential, discrete Rayleigh, and discrete Weibull distributions show that the DNGWD attains the lowest reported Akaike information criterion value among the candidate models. These findings indicate that the proposed distribution offers a potentially useful framework for modelling discrete lifetime and actuarial count data.