Estimation of different types of entropies for the Kumaraswamy distribution

• Published in: PloS one Vol. 16; no. 3; p. e0249027
• Main Authors: Al-Babtain, Abdulhakim A., Elbatal, Ibrahim, Chesneau, Christophe, Elgarhy, Mohammed
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 30.03.2021; Public Library of Science (PLoS)
• Subjects: Analysis; Bioinformatics; Biology and Life Sciences; Computer and Information Sciences; Cryptography; Datasets; Distribution (Probability theory); Entropy; Entropy (Information theory); Estimates; Linguistics; Maximum likelihood estimates (Statistics); Nervous system; Neurosciences; Physical Sciences; Probability distribution; Quantum computers; Random variables; Research and Analysis Methods; Social Sciences; Saudi Arabia; Riyadh Saudi Arabia
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0249027

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. 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.