Kernel Estimation of Mathai-Haubold Entropy and Residual Mathai-Haubold Entropy Functions under α-Mixing Dependence Condition

Abstract

Mathai and Haubold introduced a new generalized entropy namely Mathai-Haubold entropy and Dar and Al-Zahrani proposed the Mathai-Haubold entropy for the residual life time and called it as residual Mathai-Haubold entropy. In the present paper, we propose nonparametric estimators for the Mathai-Haubold entropy and the residual Mathai-Haubold entropy where the observations under consideration are exhibiting α-mixing (strong mixing) dependence condition. Asymptotic properties of the estimators are established under suitable regular conditions. A Monte Carlo simulation study is carried out to compare the performance of the estimators using the mean squared error. The methods are illustrated using a real data set.

KEYWORDS AND PHRASES:

• Mathai-Haubold entropy
• residual Mathai-Haubold entropy
• kernel estimator
• α-mixing

Acknowledgment

The authors express their gratefulness for the constructive criticism of the learned referees which helped to improve considerably the revised version of the paper.