Mathematics and Statistics Vol. 11(2), pp. 263 - 276
DOI: 10.13189/ms.2023.110204
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Estimation of the Location Parameter of Cauchy Distribution Using Some Variations of the Ranked Set Sampling Technique

Arwa Salem Maabreh ¹, Mohammad Fraiwan Al-Saleh ^1,2,*
1 Department of Statistics, Yarmouk University, Jordan
² Department of Mathematics & Statistics, Jordan University of Science and Technology, Jordan

ABSTRACT

It is well known that ranked set sampling (RSS) technique and its variations, when applicable, are more efficient for estimating the population mean than the usual random sampling techniques. Despite the fascinating applications of Cauchy distribution, it has many unusual properties. For example: its moments either don’t exist or exist but are infinite, and its minimal sufficient statistics are just the order statistics. Given that the shape of the Cauchy distribution is similar to the normal one, it would be advantageous to carry out some statistical studies to focus on estimating its parameters; in particular the location parameter which is the median. In this paper, the estimation of the location parameter of the Cauchy distribution using RSS and some of its variations; namely, Double RSS, Median RSS, Multistage RSS, and Steady-State RSS are considered. The estimators are compared with each other and with their counterparts using simple random sampling (SRS). The findings show that RSS or any of its variations, being evaluated in this study, is more efficient in estimating the location parameter compared to SRS. The comparison among the RSS variations reveals that the steady-state RSS is more efficient than other RSS variations. Moreover, to overcome some of the challenges of Cauchy distribution, such as the non-existence of moments, a truncated Cauchy distribution is used. For this distribution, all moments are finite as well as the moments of order statistics. Results show that RSS and Median RSS outperform the SRS in estimating the location parameter, even with the truncated version of Cauchy. Overall, the work of this paper identifies other advantages of RSS techniques.

KEYWORDS
Cauchy Distribution, Double Ranked Set Sampling, Median Ranked Set Sampling, Multistage Ranked Set Sampling, Ranked Set Sampling, Simple Random Sampling, Steady State Ranked Set Sampling, Truncated Cauchy Distribution

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Arwa Salem Maabreh , Mohammad Fraiwan Al-Saleh , "Estimation of the Location Parameter of Cauchy Distribution Using Some Variations of the Ranked Set Sampling Technique," Mathematics and Statistics, Vol. 11, No. 2, pp. 263 - 276, 2023. DOI: 10.13189/ms.2023.110204.

(b). APA Format:
Arwa Salem Maabreh , Mohammad Fraiwan Al-Saleh (2023). Estimation of the Location Parameter of Cauchy Distribution Using Some Variations of the Ranked Set Sampling Technique. Mathematics and Statistics, 11(2), 263 - 276. DOI: 10.13189/ms.2023.110204.