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

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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.

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Acknowledgements

The authors thank the reviewers and the editor for helpful comments that have improved the paper. The first author is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) 2211/A National PhD scholarship program and the Higher Education Council of Turkey (YÖK) 100/2000 PhD scholarship program.

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Authors and Affiliations

  1. The Graduate School of Natural and Applied Sciences, Dokuz Eylul University, Tinaztepe Campus, 35160, Buca, Izmir, Turkey

    Yusuf Can Sevil

  2. Department of Statistics, Faculty of Science, Dokuz Eylul University, Tinaztepe Campus, 35160, Buca, Izmir, Turkey

    Tugba Ozkal Yildiz

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  1. Yusuf Can Sevil
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  2. Tugba Ozkal Yildiz
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Appendices

Appendices

See Table 4.

Table 4 Values of \(c_{\psi }\), \(\psi = \hbox {SRS}\), RSS, GMRSS (\(r=1\)), GMRSS (\(r=k\)) and ERSS
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Sevil, Y.C., Yildiz, T.O. Gumbel’s bivariate exponential distribution: estimation of the association parameter using ranked set sampling. Comput Stat 37, 1695–1726 (2022). https://doi.org/10.1007/s00180-021-01176-2

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