Computes parametric bootstrap confidence intervals for unknown model parameters and reliability \(R\), based on maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), and maximum product of spacing estimation (MPS).
parametric_bootstrap(
est.method,
opt.method,
boot.estimates,
n,
B = 1000,
seed = NULL,
one.step = TRUE,
alpha = 0.05
)Character string specifying the estimation method used.
Options include "MLE", "LSE", "WLSE", and "MPS".
Character string specifying the optimization method used in optim.
Common options include "Nelder-Mead", "BFGS", "CG",
"L-BFGS-B", "SANN", and "Brent".
A named list of initial parameter estimates. The elements \((a_1, b_1, \lambda_1)\) correspond to the strength variable, \((a_2, b_2, \lambda_2)\) correspond to the stress variable, and \(\theta\) is the Clayton copula dependence parameter.
Integer. Sample size.
Integer. Number of bootstrap replications.
Integer. Random seed for reproducibility.
Logical. If TRUE, one-step LSE and WLSE estimators
are used for \(\theta\).
Numeric. Significance level for confidence intervals
(e.g., 0.05 for a \(95\%\) confidence interval).
A list containing:
A numeric matrix with lower and upper \(100(1-\alpha)\%\) bootstrap percentile confidence limits.
A matrix of bootstrap estimates for all parameters over \(B\) replications.
This function implements a parametric bootstrap percentile method to construct confidence intervals for unknown parameters and reliability \(R\) under different estimation methods (MLE, LSE, WLSE, and MPS).
Further theoretical details are provided in Kizilaslan (2026).
Kizilaslan, F. (2026). Reliability estimation in dependent stress–strength model with Clayton copula and modified Weibull margins. arXiv:2604.12130