Estimation of Tsallis entropy and its applications to goodness-of-fit tests

TL;DR

This paper develops and compares multiple estimators for Tsallis entropy and divergence, demonstrating their effectiveness in goodness-of-fit testing for distributions like normal and exponential, with applications to censored data and real datasets.

Contribution

It introduces new estimators for Tsallis entropy, analyzes their properties, and applies them to develop goodness-of-fit tests, including for censored data, outperforming existing methods.

Findings

Proposed estimators show low bias and MSE in simulations.

New goodness-of-fit tests perform well compared to existing tests.

Estimator robustness to outliers is demonstrated through simulations.

Abstract

In this paper, we consider the problem of estimating Tsallis entropy from a given data set. We propose four different estimators for Tsallis entropy measure based on higher-order sample spacings, and then discuss estimation of Tsallis divergence measure. We compare the performance of the proposed estimators by means of bias and mean squared error and also examine their robustness to outliers. Next, we propose a spacings-based estimator for Tsallis entropy under progressive type-II censoring and study its performance using Monte Carlo simulations. Another estimator for Tsallis entropy is proposed using quantile function and its consistency and asymptotic normality are studied, and its performance is evaluated through Monte Carlo simulations. Goodness-of-fit tests for normal and exponential distributions as applications are developed using Tsallis divergence measure. The performance of the proposed tests are then compared with some known tests using simulations and it is shown that the proposed tests perform very well. Also, an exponentiality test under progressive type-II censoring is proposed, its performance is compared with an existing entropy-based test using simulation. It is observed that the proposed test performs well. Finally, some real data sets are analysed for illustrative purposes.