International Journal of Sciences: Basic and Applied Research (IJSBAR) ISSN 2307-4531 (Print & Online) http://gssrr.org/index.php?journal=JournalOfBasicAndApplied --------------------------------------------------------------------------------------------------------------------------- 284 Estimation of Cauchy Parameters under Ranked Set Sampling Sameer Ahmad Hasan Al-Subh * Department of Mathematics and Statistics, Mutah University, Karak, Jordan Email: salsubh@yahoo.com Abstract In this paper, we will consider the MLEs (maximum likelihood estimators), and meds (median estimators) of the parameters of the Cauchy distribution using SRS (simple random sample) and RSS (ranked set sample). A comparison between these estimators using bias, MSE (mean square error) and the efficiency will be done using simulation. It appears that the MLE based on RSS can be a real competitor to the MLE based on SRS. Keywords: Ranked set sampling; Simple random sampling; parameters; Cauchy distribution; maximum likelihood estimator; bias; mean square error. 1. Introduction The Cauchy distribution is one of the interesting continuous distributions. There are many areas of application of the Cauchy distribution including economic modeling (time series analysis, stock and commodity price changes, and sales), theory of atomic and nuclear transitions and the Brownian motion tend to a Cauchy distribution. The Cauchy distribution gains its importance by giving a good approximation to the normal distribution. ------------------------------------------------------------------------ * Corresponding author.