Statistical inference and optimal plans for improved adaptive type-II progressive censored data following Kumaraswamy-G family of distributions

Abstract The present paper attempts to study the parametric inference for Kumaraswamy's generalized family of distribution under an improved adaptive Type-II progressive censored sample. Under the frequentist approach, maximum likelihood estimates and maximum product spacing estimates of unknown model parameters are computed using Newton-Raphson methods. The existence and uniqueness properties of maximum likelihood estimates are deduced. Approximate confidence intervals for parameters are created via a variance-covariance matrix and bootstrap resampling methods. Under squared error and LINEX loss function, the Bayes estimates are investigated using independent gamma priors distribution for the unknown parameters. The Markov Chain Monte Carlo (MCMC) approximation technique has been used to compute the Bayes estimates and produce the highest posterior density credible intervals. The efficacy of the suggested approach is assessed using an extensive simulation study. The convergence of the MCMC sample is judged through the different diagnostic plots. Three optimality criteria have been presented to choose the most suitable progressive scheme from various sampling plans. A real-life situation representing the tensile strength of polyester fibres is used to show the application of the recommended work in a real-world scenario.