Kendall's Tau-based Estimation of the Clayton Copula Parameter

Estimates the dependence parameter \(\theta\) of the Clayton copula using Kendall's tau-based moment estimator.

theta_Ktau_estimate(data)

Arguments

data

A list containing two numeric vectors: X (strength) and Y (stress).

Value

A numeric scalar giving the estimate of \(\theta\) based on Kendall's tau (\(\tau\)).

Details

Kendall's Tau Estimator for the Clayton Copula Parameter

The estimator is derived from the relationship between Kendall's tau and the Clayton copula parameter: \(\tau = \theta / (\theta + 2)\).

Examples

set.seed(123)
n <- 50
a1 <- 0.75; b1 <- 1.5; lambda1 <- 0.6
a2 <- 1.2; b2 <- 0.5; lambda2 <- 0.9
theta <- 5 # 1, 2, 3, 4
# data generation
dat <- SSReliabilityClaytonMWD::rMweibull_Clayton(n, a1, b1, lambda1, a2, b2, lambda2, theta)
theta_Ktau_estimate(dat)
#> [1] 4.920904