Numerical analysis of the accuracy of bivariate quantile distributions utilizing copulas compared to the GUM supplement 2 for oil pressure balance uncertainties | International Journal of Metrology and Quality Engineering (IJMQE)

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Table 4

Specification of common parameter based bivariate copula families (Adapted from Goda [17]). In our particular problem the variable u corresponds to the random variable and the variable v corresponds to the random variable ξ_λ so that the bivariate copula C (u, v) can be used to construct the joint probability density function as for convenience.

Copula name	Copula function C (u, v)	Copula parameter relationship with Kendall's tau
Normal
Student-t
Gumbel		and θ ≥ 1
Frank
Clayton		and θ ∈ [0, ∞]

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