Estimation of different types of entropies for the Gumbel Type-2 distribution

Povzetek

The estimation of the entropy of a random system is relevant in many scientific applications. This article is aimed at the analysis of the entropy of the Gumbel type-2 distribution, an aspect of the statistical analysis which has not been employed. On this basis, six different entropy measures are considered and expressed analytically. A numerical study is performed to discuss the behavior of these measures. In addition, we considered the method of maximum likelihood estimation approach to obtain the parameter estimates of the Gumbel type-2 distribution. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.