General Distribution Theory of the Concomitants of Order Statistics

Su, Yang

doi:10.1214/aos/1176343954

Cited by 109 publications

(46 citation statements)

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“…The round bracket on a subscript is used to indicate that the ordering is perfect, while the square bracket is used to indicate that the ordering is imperfect. Yang (1977) has shown that the conditional distribution of the concomitant variable X…”

Section: Second Modification Of Bvrss (Mbvrss2)mentioning

confidence: 99%

Other approaches to bivariate ranked set sampling

Al-Saleh

Alshboul

2018

CSAM

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Ranked set sampling, as introduced by McIntyre (Australian Journal of Agriculture Research, 3, 385-390, 1952), dealt with the estimation of the mean of one population. To deal with two or more variables, different forms of bivariate and multivariate ranked set sampling were suggested. For a technique to be useful, it should be easy to implement in practice. Bivariate ranked set sampling, as introduced by Al-Saleh and Zheng (Australian & New Zealand Journal of Statistics, 44, 221-232, 2002), is not easy to implement in practice, because it requires the judgment ranking of each of the combination of the order statistics of the two characteristics. This paper investigates two modifications that make the method easier to use. The first modification is based on ranking one variable and noting the rank of the other variable for one cycle, and do the reverse for another cycle. The second approach is based on ranking of one variable and giving the second variable the same rank (Concomitant Order Statistic) for one cycle and do the reverse for the other cycle. The two procedures are investigated for an estimation of the means of some well-known distributions. It is show that the suggested approaches can be used in practice and can be more efficient than using SRS. A real data set is used to illustrate the procedure.

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Section: Second Modification Of Bvrss (Mbvrss2)mentioning

confidence: 99%

Other approaches to bivariate ranked set sampling

Al-Saleh

Alshboul

2018

CSAM

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“…, p. Note that the ε (i) 's are also concomitants of the y (i) . It is clear that the ε i 's are iid and that (see Yang 1977) they are independent with mean 0 when the order statistics, y (i) , ε (i) , and m(y (i) ) depend on n and should be de-…”

Section: A Brief Description Of Sliced Inverse Regressionmentioning

confidence: 99%

Sliced Inverse Regression

Li¹

2014

Wiley StatsRef: Statistics Reference Online

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“…After remarkable work in 1973 by David and Galambos (1974) and David et al (1977) deduced the asymptotic theory of concomitants of order statistics and distribution and expected value of the rank of a concomitant of an order statistics, respectively. Yang (1977) discussed the general distribution theory of the concomitants of order statistics. Bhattacharya (1984), in his paper, Induced order statistics: Theory and applications, explained the theory and application of concomitant of order http://journals.uob.edu.bh statistics in the name of induced order statistics.…”

Section: Introductionmentioning

confidence: 99%

Order Statistics from Bivariate Log-Exponentiated Kumarswamy Distribution

Khan¹

2017

IJCTS

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Abstract:In this article, the distribution of concomitant of order statistics has been obtained from Bivariate log-exponentiated Kumarswamy distribution. The distribution of the th r order statistics and it's concomitant arising from Bivariate log-exponentiated Kumarswamy distribution has been deduced. The properties of concomitant arising from the corresponding order statistics are used to derive the results. The moment generating function (mgf) of concomitant of order statistics is also derived. We have also obtained the expression for the joint distribution of concomitants of two non-adjacent order statistics.

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General Distribution Theory of the Concomitants of Order Statistics

Cited by 109 publications

References 0 publications

Other approaches to bivariate ranked set sampling

Other approaches to bivariate ranked set sampling

Sliced Inverse Regression

Order Statistics from Bivariate Log-Exponentiated Kumarswamy Distribution

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