A new family of generalized distributions based on Modi-G transformation, with applications in Epidemiology, Engineering, and Environmental Science

This paper introduces the New Generalized Modi-G Transformation (NGMT) family, a parsimonious ratio-based framework designed to enhance the flexibility of baseline probability distributions without the algebraic complexity of incomplete beta or gamma functions. We develop the NGMT-Exponential (NGMTE) distribution, introducing two shape parameters ( α and β ) and a scale parameter ( λ ) to effectively model diverse hazard rates, including bathtub and non-monotonic shapes. Fundamental mathematical properties, including the hazard function, quantile function, and moments, are derived. To identify the most reliable parameter estimation strategy, 15 non-Bayesian methods were evaluated via Monte Carlo simulations across sample sizes n = 15 to n = 350 . Quantitative results reveal that while the Least Squares (LS) method is a common estimator, it yields higher Mean Squared Errors (MSE) in small samples compared to the Minimum Spacing Absolute Distance (MSAD) estimator, which proved most accurate for n = 15 . As sample size increases, the Maximum Likelihood (MLE) and Maximum Product of Spacings (MPS) methods demonstrate superior consistency. Empirical applications confirm the NGMTE’s superior fit, consistently achieving optimal metrics: Epidemiology (AIC = 245.18, BIC = 251.44, HQIC = 247.65, p = 0 . 941 ), Engineering (AIC = 188.42, BIC = 194.10, HQIC = 190.58, p = 0 . 978 ), and Environmental Science (AIC = 412.30, BIC = 418.04, HQIC = 414.49, p = 0 . 992 ).