Estimation of Matusita measure between generalized inverted exponential distributions under progressive first-failure censored data

Inference for Matusita measure between independent generalized inverted exponential distributions (GIEDs) is investigated under progressive first-failure censoring. When both GIEDs have common scale but different shape parameters, maximum likelihood estimator of the Matusita measure along with the existence and uniqueness of model estimators are established. Approximate confidence interval is constructed in conse-quence. Alternative generalized point and interval estimates are further constructed based on proposed pivotal quantities. For comparison, bootstrap confidence intervals are also provided. In addition, likelihood and generalized estimates for the Matusita measure are also discussed when two GIEDs have unequal parameters. Further, likelihood ratio testing is provided for comparing the equivalence of the interested parameters. Finally, extensive simulation studies are carried out to evaluate the performances of different methods, and two real life examples are presented for application.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper investigates the inference for the Matusita measure between independent Generalized Inverted Exponential Distributions (GIEDs) under progressive first-failure censoring. The maximum likelihood estimator for the Matusita measure is established when the GIEDs have a common scale but different shape parameters, along with the existence and uniqueness of model estimators. An approximate confidence interval and alternative point and interval estimates based on proposed pivotal quantities are constructed. Bootstrap confidence intervals are also provided for comparison. Additionally, likelihood and generalized estimates for the Matusita measure are discussed when the two GIEDs have unequal parameters. Likelihood ratio testing is provided for comparing the equivalence of the interested parameters. Extensive simulation studies are conducted to evaluate the performances of different methods, and two real-life examples are presented for application.