A Flexible Extension of Ibrahim distribution: Properties and Application

This paper introduces a novel and flexible probability distribution tailored to model complex real-world phenomena, particularly those exhibiting skewness, heavy tails, or bimodal behavior. The proposed distribution is defined for x > 0 and governed by three key parameters: β, λ, and α. The density function is formulated using α combination of exponential and quadratic exponential terms, providing a rich structure that allows for enhanced modeling capabilities. Notably, the distribution generalizes well-known models such as the exponential and Rayleigh distributions through the parameters α and β. Its flexibility enables it to accommodate both monotonic and non-monotonic hazard rates, making it particularly suitable for reliability and survival analysis. Moreover, the λ parameter introduces a mechanism for bias correction, which is essential for capturing asymmetric data patterns. The statistical properties of the distribution, including its moments, quantiles, and hazard functions, are analytically derived. Parameter estimation is conducted via the maximum likelihood method. Simulation studies and empirical applications confirm the distribution’s superior performance over traditional models, especially in handling skewed and heavy-tailed datasets. DOI : https://doi.org/10.52783/pst.1853