The Binosson Distribution: A Unified Probabilistic Framework Bridging the Binomial and Poisson Models

Classical Binomial and Poisson distributions, constrained by fixed trials and static event rates, falter in modeling modern datasets with dynamic parameters or contextual dependencies (e.g., variable infection rates, covariate-influenced risks). This paper introduces the Binosson Distribution, a hybrid framework unifying Binomial trials and Poisson processes through dynamic parameterization of trial counts (n) and designed to address event rates (λ). The distribution has been proposed to bridge the gap between these two distributions, incorporating aspects of both. Binomial-cum-Poisson distributions are modified to obtain a distribution that will be able to solve the probability problems that lies between the two distributions. Binosson is the result from the product of Binomial and Poisson distributions. Statistical properties such as mean, variance, standard deviation, skewedness and kurtosis were also derived.