Statistical Inference for Rayleigh Distribution Using Ranked Set Sampling: A Bayesian Approach

Fahad M. Al Subhi¹

1. Dept. of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia.

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.4 , pp.1-13, Aug-2024

Online published on Aug 31, 2024

Copyright © Fahad M. Al Subhi . 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 :
Working on symmetrical or asymmetrical data is complicated since each requires a different probability density function. Many statistical distributions can be used for these data types, where choosing one should be satisfied with the correct data type. So, we apply the ranked set sampling technique, which is essential in gaining data when dealing with units in a population is expensive. However, their classification is simple according to the variable of interest. The Rayleigh distribution has recently played a crucial role in analyzing symmetrical or asymmetrical complex data sets specifically in modeling claim and risk data used in actuarial and financial studies, and its density can take different symmetric and asymmetric possible shapes. It is proposed in various areas, such as reliability, survival, economics, actuarial science, and insurance. In this paper, we provide Bayesian estimation for a parameter of the Rayleigh distribution based on a simple random sample (SRS) and ranked set sampling (RSS) using two loss functions; the squared error loss function, and the linex loss function. The results of the simulation study showed that the Bayes estimates based on RSS are more efficient than the estimates based on SRS for different sample sizes of (n) and different values of the parameter ?.

Key-Words / Index Term :
Bayesian analysis; Linex loss function; Ranked set sampling; Rayleigh distribution; Squared error loss function; Simulation Study

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