A New Application of DUS Transformation on X-shanker Distribution with Real Data Sets

Abstract

 This research presents a new development in probability distribution modeling by applying the DUS transformation to the X-Shanker distribution, resulting in a modified distribution known as the truncated X-Shanker distribution under the DUS transformation. This modification aims to enhance the flexibility and efficiency of the distribution in representing real-world data.

The behavior of the probability density function and the cumulative distribution function of the new distribution has been analyzed and compared with the original distribution. Additionally, its structural properties, such as mean, variance, moment functions, and reliability function, have been derived. The parameters of the new distribution have been estimated using the maximum likelihood estimation (MLE) method to ensure accurate parameter estimation.

To evaluate the performance of the proposed distribution, it has been applied to real-world datasets, where the results showed that the new distribution provides a better fit for the data compared to traditional probability models. This study highlights the importance of using the DUS transformation in improving probability distributions and expanding their applicability in statistical analysis and applied data studies