On the Generalized Version of the Extended Standard \(U\)-Quadratic Distribution

This paper introduces the Generalized extended Standard U-quadratic (GeSU) distribution, an extension of the extended Standard U-quadratic (eSU) distribution, developed by incorporating an additional parameter. The GeSU distribution effectively models asymmetric data exhibiting bathtub and inverted bathtub shapes over the unit interval [0,1]. Several special cases of the proposed distribution are also derived. Key statistical properties, including moments, the moment-generating function, mean, variance, median, mode, skewness, and kurtosis, are established, along with a random number generation algorithm. The performance of maximum likelihood estimation for the parameters of the GeSU distribution is assessed through simulation studies. Furthermore, the distribution is applied to a real dataset, demonstrating a superior fit compared to the eSU, Unit-Rayleigh, and Unit-Burr XII distributions. These results highlight the flexibility and applicability of the proposed GeSU distribution in modeling unit-interval data.