Inference on the Kumaraswamy distribution

Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. The Kumaraswamy distribution is one of these distributions which is particularly useful to many natural phenomena whose outcomes have lower and upper bounds or bounded outcomes in the biomedical and epidemiological research. This article studies point estimation and interval estimation for the Kumaraswamy distribution. The inverse estimators (IEs) for the parameters of the Kumaraswamy distribution are derived. Numerical comparisons with maximum likelihood estimation and biased-corrected methods clearly indicate the proposed IEs are promising. Confidence intervals for the parameters and reliability characteristics of interest are constructed using pivotal or generalized pivotal quantities. Then, the results are extended to the stress–strength model involving two Kumaraswamy populations with different parameter values. Construction of confidence intervals for the stress–strength reliability is derived. Extensive simulations are used to demonstrate the performance of confidence intervals constructed using generalized pivotal quantities.