Abstract :

In This Paper, We Propose A New Extended Rayleigh Distribution (NERD) And Explore Its Theoretical And Practical Significance In Statistical Modelling. The NERD Is Formulated As A Flexible Generalization Of The Classical Rayleigh Distribution By Introducing An Additional Shape Parameter, Thereby Enhancing Its Ability To Model A Wider Variety Of Real-world Phenomena, Particularly In Lifetime And Reliability Data Analysis. We Rigorously Define The Distribution And Derive Several Important Statistical Properties, Including The R-th Moments, Moment Generating Function (MGF), Characteristic Function (CF), And Cumulant Generating Function (CGF). These Properties Not Only Provide Insight Into The Behaviour Of The Distribution But Also Facilitate Its Application In Inferential And Applied Statistics. To Estimate The Unknown Parameters Of The NERD, We Employ The Maximum Likelihood Estimation (MLE) Method. Key Words: Distribution; Rayleigh; Reliability; Hazard Function; Maximum Likelihood Estimation

Published:

25-9-2025

Issue:

Vol. 25 No. 9 (2025)

Page Nos:

531-540

Section:

Articles

License:

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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