Progressive Type-II Censored Samples for Bivariate Weibull Distribution with Economic and Medical Applications

Recently, the Bivariate Weibull distribution based on different copula functions has received considerable attention in the statistical literature. For progressive Type-II censored samples of bivariate distribution, the effective sample size of censored sample \(m\) is fixed; the progressive censoring scheme is provided during the experiment for one variable and the second variable concomitant it. The Farlie–Gumbel–Morgenstern (FGM) copula has been used to construct the Bivariate Weibull distribution, which is called FGM Bivariate Weibull (FGMBW) distribution. In this paper, we consider the point, and interval estimation of the unknown parameters of the FGM bivariate Weibull distribution based on progressive Type-II censored samples. Two bootstrap confidence intervals are also proposed. In addition, two real data sets have been introduced and analyzed to examine the model in practice. A simulation study has been conducted to compare the preferences between different censoring schemes.