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Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling

Yusuf Can Sevil and Tugba Ozkal Yildiz
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Yusuf Can Sevil: Dokuz Eylul University
Tugba Ozkal Yildiz: Dokuz Eylul University

Computational Statistics, 2022, vol. 37, issue 4, No 6, 1695-1726

Abstract: Abstract In this paper, we consider three sampling methods that are ranked set sampling (RSS), generalized modified ranked set sampling (GMRSS) and extreme ranked set sampling (ERSS). RSS and ERSS are well-known sampling schemes. In GMRSS procedure, a single ranked unit is selected for full measurement. This paper improves estimators based on RSS, GMRSS and ERSS for association parameter of type-I Gumbel’s bivariate exponential distribution (GBED-I) by using maximum likelihood (ML) estimation. To determine whether there is a statistically significant association between the components, we investigate likelihood ratio tests based on RSS, MRSS and ERSS. To examine the performances of suggested estimators and tests with respect to their counterparts of simple random sampling (SRS), we provide an extensive Monte Carlo simulation. According to the results, it appears that GMRSS provides a more efficient ML estimator than the other sampling methods when only the maximum ranked units are selected. Also, it is observed that the test statistic based on GMRSS has the highest power among the test statistics when the sample is obtained from the maximum ranked units. Considering that GMRSS can be obtained with less effort than other samples, these results become even more meaningful.

Keywords: GBED-I; Association parameter; Ranked set sampling; Maximum likelihood estimation; Algorithm for sampling; Likelihood ratio test; Type-I error; Power of test (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00180-021-01176-2

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