A new two-parameter family of discrete distributions

This paper introduces a new family of discrete distributions with two shape parameters, termed the Generalized Two-Parameter Discrete Distribution (GTPDD). The raw and central moments are derived from a general expression for its <i>r</i>th factorial moments. Additionally, the paper provides expressions for the moment generating function, coefficient of variation, skewness, kurtosis, index of dispersion and the hazard function. Parameter estimation is addressed using the maximum likelihood estimation method, and the uniqueness of the maximum likelihood estimators is also verified. The applicability of the proposed distribution is illustrated through the modeling of two real data sets, one from engineering and the other from survival analysis.