Random Generation for MWD Marginals via Clayton Copula

Generates bivariate random samples from a dependent stress–strength model where both marginals follow the Modified Weibull Distribution (MWD), and the dependence structure between the variables is modeled using a Clayton copula.

Generates bivariate random samples from a dependent stress–strength model where both marginals follow the Modified Weibull Distribution (MWD), and dependence between variables is modeled using a Clayton copula.

rMweibull_Clayton(n, a1, b1, lambda1, a2, b2, lambda2, theta)

Arguments

n

Integer. Number of observations to be generated.

a1, b1, lambda1

Parameters of the strength variable \(X\), with \(a_1 > 0\), \(b_1 \ge 0\), and \(\lambda_1 \ge 0\).

a2, b2, lambda2

Parameters of the stress variable \(Y\), with \(a_2 > 0\), \(b_2 \ge 0\), and \(\lambda_2 \ge 0\).

theta

Clayton copula dependence parameter, \(\theta > 0\).

Value

A list containing:

A list containing:

U

Uniform samples used in the copula construction.

V

Dependent uniform samples generated via the Clayton copula.

X

Simulated observations from \(X \sim \mathrm{MWD}(a_1, b_1, \lambda_1)\) obtained by transforming \(U\).

Y

Simulated observations from \(Y \sim \mathrm{MWD}(a_2, b_2, \lambda_2)\) obtained by transforming \(V\).

Details

Bivariate Random Data Generation under Clayton Copula with MWD Marginals

This function generates dependent uniform variables using the Clayton copula, which are then transformed via inverse CDFs of the Modified Weibull marginals to obtain \((X, Y)\).

Further details are provided in Kizilaslan (2026).

References

Kizilaslan, F. (2026). Reliability estimation in dependent stress–strength model with Clayton copula and modified Weibull margins. arXiv:2604.12130

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 <- 1 # 2, 3, 4, 5
# data generation
dat <- rMweibull_Clayton(n, a1, b1, lambda1, a2, b2, lambda2, theta)
str(dat)
#> List of 4
#>  $ U: num [1:50] 0.288 0.788 0.409 0.883 0.94 ...
#>  $ V: num [1:50] 0.0726 0.6101 0.7749 0.3214 0.7372 ...
#>  $ X: num [1:50] 0.485 1.062 0.617 1.231 1.388 ...
#>  $ Y: num [1:50] 0.00392 0.33629 0.56182 0.08896 0.50229 ...