Length-Biased Distribution for Family of Life-Time Testing Models and its Properties

Surinder Kumar¹ , Shivendra Pratap Singh² , Bhupendra Meena³ , Rahul Shukla⁴

1. Dept. of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.
2. Dept. of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.
3. Dept. of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.
4. Dept. of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.6-13, Jun-2024

Online published on Jun 30, 2024

Copyright © Surinder Kumar, Shivendra Pratap Singh, Bhupendra Meena, Rahul Shukla . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Our research introduces a new lifetime distribution family called Length-Biased Lifetime Distribution, which is based on length bias. To comprehend the nature of the suggested distribution, we take into account its many statistical aspects, such as its reliability, hazard function and other characteristics. Also, to estimate the parameters of the suggested distribution, we have utilized the ML technique. The Lorenz and Bonferroni curves, Shannon’s entropy, and Renyi entropy are also obtained. Using two real-life datasets, we evaluate the suggested distribution’s performance to that of competing distributions.

Key-Words / Index Term :
Entropy, Hazard Function, Length-Biased Distribution, Maximum Likelihood Estimation, Reliability, Reversed Hazard Function, Order Statistic.

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