Varentropy estimators applied to goodness of fit tests for the Gumbel distribution

The Gumbel distribution is one of the most used models to carry out risk analysis in extreme events, in reliability tests, and in life expectancy experiments. Recently, Alizadeh and Shafaei (J Stat Comput Simul 15:2582–2599, 2023) investigated varentropy of a continuous random variable and introduced some estimators for it. The present article applies these estimators and construct some tests for Gumbel distribution. Percentage points of the new test statistics are obtained and then power values of the proposed tests against various alternatives are computed. The results of a simulation study show that the tests have a good performance in terms of power. Finally, two real data sets are used to illustrate the application of the proposed tests.