Robust Estimators and Test-Statistics for One-Shot Device Testing Under the Exponential Distribution

TL;DR

This paper introduces robust minimum density power divergence estimators and Z-type test statistics for one-shot device testing under the exponential distribution, improving robustness over traditional methods.

Contribution

It develops a new family of estimators and test statistics based on MDPDEs, enhancing robustness in one-shot device testing models.

Findings

Some MDPDEs outperform MLE in robustness.

Z-type tests based on MDPDEs are more robust than classical Z-tests.

Simulation results confirm improved robustness of proposed methods.

Abstract

This paper develops a new family of estimators, the minimum density power divergence estimators (MDPDEs), for the parameters of the one-shot device model as well as a new family of test statistics, Z-type test statistics based on MDPDEs, for testing the corresponding model parameters. The family of MDPDEs contains as a particular case the maximum likelihood estimator (MLE) considered in Balakrishnan and Ling (2012). Through a simulation study, it is shown that some MDPDEs have a better behavior than the MLE in relation to robustness. At the same time, it can be seen that some Z-type tests based on MDPDEs have a better behavior than the classical Z-test statistic also in terms of robustness.