Construction of bivariate asymmetric copulas

Mukherjee, Saikat; Lee, Youngsaeng; Kim, Jong Min; Jang, Jun Hwan; Park, Jeong‐Soo

doi:10.29220/csam.2018.25.2.217

Cited by 7 publications

(11 citation statements)

References 27 publications

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“…More precise, for a given symmetric or radial symmetric copula S, we determine copulas for which S is the prescribed symmetrized or the radial symmetrized part. Comparing to well known results on this topic in literature, mainly to [18] where are developed some analytical methods of construction of bivariate asymmetric copulas, and [16] where was treated the multivariate case, our new class of copulas seems simple, handier more understandable.…”

Section: Introductionmentioning

confidence: 79%

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

Maazouz¹,

Sani²

2023

Moroccan Journal of Pure and Applied Analysis

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New copulas, based on perturbation theory, are introduced to clarify a symmetrization procedure for asymmetric copulas. We give also some properties of the symmetrized copula mainly conservation of concordance. Finally, we examine some copulas with a prescribed symmetrized part. The start point of the treatment is the independence copula and the last one will be an arbitrary member of Farlie-Gumbel-Morgenstein family. By the way, we study topologically, the set of all symmetric copulas and give some of its classical and new properties.

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Section: Introductionmentioning

confidence: 79%

New asymmetric perturbations of FGM bivariate copulas and concordance preserving problems

Maazouz¹,

Sani²

2023

Moroccan Journal of Pure and Applied Analysis

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“…Crosier 20 stated that the choice of

k = \frac{D}{2}

where

D = \sqrt{{(μ_{1} - μ_{0})}^{'} {normalΣ}^{- 1} false(μ_{1} - μ_{0} false)}

is the minimum ARL at D for a given in‐control ARL. The control chart statistic for MCUSUM chart is

Y_{i} = {([], {boldS}^{'}_{i} Σ^{- 1} S_{i})}^{1 / 2}, i = 1, 2, 3, \dots

where h is the control limit.…”

Section: The Multivariate Cumulative Sum (Mcusum) Control Chartmentioning

confidence: 99%

“…In addition, Liebscher 19 provided two methods of constructing based on multivariate copulas and explored the properties of copula's families. Finally, Mukherjee et al 20 provided a method of construction a new type of bivariate asymmetric copulas which can be used in many fields. As mentioned above, Nidsunkid et al 10 explored the sensitivity of multivariate Shewhart and MEWMA control chart performances when the normality assumption is violated.…”

Section: Introductionmentioning

confidence: 99%

The effects of constructed bivariate copulas on multivariate control charts effectiveness

Sukparungsee

Sasiwannapong

Busababodhin

et al. 2021

Quality & Reliability Eng

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The average control chart monitors the shifts in the process. The familiar multivariate control charts are used to detect the mean vector of the process such as multivariate cumulative sum (MCUSUM) and Hotelling's T2 control charts. In this paper, the effects of constructing bivariate copulas on multivariate control charts, that is, MCUSUM and Hotelling's T2 control charts are intensively investigated when observations are drawn from the exponential distribution. Moreover, the dependence levels of observations are classified to be weak, moderate, and strong in both positive and negative values by Kendall's tau. The numerical results were obtained by Monte Carlo simulation to explore the average run length (ARL). The simulation results show that the performance of Hotelling's T2 control chart is superior to the MCUSUM control chart for all shifts in the mean vector of process. Furthermore, from applying the presented control chart to two sets of real data, data set of the strength of 1.5 cm glass fibers measured at the National Physical Laboratory, England and data set of the strength of glass of the aircraft window, it was found that for a small shift (δ≤0.1), the MCUSUM control chart is better than Hotelling's T2 control chart.

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“…[6] explored the theoretical approach of generating copulas via analytical means and gave mathematical treatment to the proposed copula models. [7] discussed the method of constructing bivariate asymmetric copulas. [8] introduced a generalized multiple-step procedure for the full inference of the directional dependence structure.…”

Section: Introductionmentioning

confidence: 99%