Some new tests for exponentiality under length-biased sampling

In this paper, based on the introduction of some estimators for the Gini index, we propose various test statistics for testing exponentiality when the data are length-biased. We investigate almost sure (a.s.) convergence of the test statistics and evaluate the performance of our proposed statistics with using a Monte Carlo simulation. We compare the powers of tests based on our proposed test statistics with those based on the test statistics introduced by Jahanshahi et al. (Citation2017) across various alternative distributions. In conclusion, the performance of the proposed tests will be assessed by applying them to two real-world datasets in a goodness-of-fit test.