Joint distribution of new sample rank of bivariate order statistics

Kemalbay, Gülder; Bayramoğlu, İsmihan

doi:10.1080/02664763.2015.1023705

Cited by 9 publications

(8 citation statements)

References 12 publications

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“…In Corollary 1, the probability mass function (PMF) of M m (1) is given by using the distribution of bivariate order statistics, see [3] and [14]. For 1 r; s n, the joint probability density function (PDF) of X r:n and Y s:n is…”

Section: Model Descriptionmentioning

confidence: 99%

An exceedance model based on bivariate order statistics

Erem¹

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In hydrologic risk analysis, the use of exceedance statistics are very important. In this sense, we construct a random threshold model based on bivariate order statistics. The exact distribution of exceedance statistics is calculated under some well-known copulas such as independent and Farlie-Gumbel-Morgenstern (FGM) copulas. Furthermore, numerical results are provided for expected value and variance of exceedance statistics under independent and Farlie-Gumbel-Morgenstern copulas. The application of the model in hydrology is also discussed.

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Section: Model Descriptionmentioning

confidence: 99%

An exceedance model based on bivariate order statistics

Erem¹

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…42 Exceedance statistics are also used in fields such as actuarial, quality control processes, and hydrology see Eryilmaz et al, 43 Triantafyllou, 1 Serinaldi et al, 44 respectively. In this manuscript, we introduce a bivariate CUSUM control chart based on exceedance statistics (BCUSUM-EX) proposed by Kemalbay and Bayramoglu 45 to monitor shifts in location parameters. The exceedance/precedence test is useful for making fast and reliable decisions because of its ease of use.…”

Section: Introductionmentioning

confidence: 99%

A bivariate CUSUM control chart based on exceedance statistics

Erem

Mahmood

2023

Quality & Reliability Eng

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In manufacturing systems, statistical process control (SPC) is used to detect unusual observations in the process. Most control charts are composed based on the normality assumptions of the observations. However, checking the normality assumption in multivariate control systems cannot be practical in real‐life applications. As a result, we propose a nonparametric bivariate cumulative sum control chart (CUSUM) based on exceedance statistics for detecting the shifts in location parameters. Since the proposed chart (BCUSUM‐EX) relied on exceedance statistics and is nonparametric, the use of the chart is straightforward and practical for users. Moreover, due to the nature of CUSUM charts, the proposed chart contains information about historical and current observations. The performance of the BCUSUM‐EX chart is compared with the spatial sign CUSUM (SS‐CUSUM) control chart under some well‐known bivariate distributions such as bivariate normal, t, and gamma. The BCUSUM‐EX chart's performance is better than the SS‐CUSUM control chart regarding run length characteristics. Lastly, to show the importance of the proposed control chart, the BCUSUM‐EX chart has been applied to the aluminium electrolytic capacitor manufacturing process.

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“…Eryilmaz and Bairamov [10] studied the distribution of the bivariate training sample ranks of OSs and its concomitants. For some recent work on this topic we can refer to [4,16]. There are some works dealing with the bivariate OSs and concomitants.…”

Section: Introductionmentioning

confidence: 99%

“…There are some works dealing with the bivariate OSs and concomitants. Kemalbay and Bayramoglu [16] considered the joint distribution of ranks of OSs based on bivariate random samples. Stoimenova and Balakrishnan [24] also dealt with the two sample problem constructing a consistent test using precedence and exceedance statistics.…”

Section: Introductionmentioning

confidence: 99%

A consistent statistical test based on bivariate random samples

Erem

Bayramoğlu

2023

Hacettepe Journal of Mathematics and Statistics

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We propose a consistent test for testing the distribution of bivariate random samples. The probability of type I, type II errors and probability of making no decisions under null and alternative hypotheses are obtained based on copula functions. The consistency of the proposed test is discussed under some null and alternative hypotheses. An unbiased, consistent estimator is proposed for probability of making no decision. Moreover, a simulation study is performed for showing the consistency of the proposed test for some well-known copulas such as independent, Clayton, Gumbel, Frank and Farlie-Gumbel-Morgenstern.

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Joint distribution of new sample rank of bivariate order statistics

Cited by 9 publications

References 12 publications

An exceedance model based on bivariate order statistics

An exceedance model based on bivariate order statistics

A bivariate CUSUM control chart based on exceedance statistics

A consistent statistical test based on bivariate random samples

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