A New Length-Biased Xrama Distribution: Properties and Application to Cancer Data

This research introduces the Length-Biased Xrama distribution, an extension of the Xrama model. The study analyzes the length-biased ‎distribution's characteristics, comparing it to the original Xrama distribution, and investigates its statistical properties like moments and relia‎bility. Furthermore, the paper explores order statistics and likelihood ratio tests and utilizes Maximum Likelihood Estimation (MLE) to ‎determine the distribution's parameters. The findings, supported by real-world cancer data applications, suggest that the Length-Biased ‎Xrama distribution provides a superior fit compared to competing distributions‎.