Estimation of the parameter of Levy distribution using ranked set sampling

Document Type : Original Article

Authors

1 Department of Statistics, Roudehen Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran

3 Department of Statistics, Allameh Tabataba'i University, Tehran, Iran.

10.22060/ajmc.2020.18499.1037

Abstract

Ranked set sampling is a statistical technique for data collection that generally
leads to more efficient estimators than competitors based on simple random sampling.
In this paper, we consider estimation of scale parameter of Levy distribution
using a ranked set sample. We derive the best linear unbiased estimator
and its variance, based on a ranked set sample. Also we compare numerically, variance of this estimator with mean square error of the maximum likelihood, a median based estimator and an estimator based on Laplace transform. It turns out that the best linear unbiased estimator based on ranked set sampling is more efficient than other mentioned estimators.

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