Product of spacing estimation of entropy for inverse Weibull distribution under progressive type-II censored data with applications

Abstract

This paper seeks to estimate the entropy for the inverse Weibull distribution using progressively Type-II censored data. To reach this objective, the entropy is defined through three entropy measures, namely, Rényi, q-entropy and Shannon entropy, and two estimation methods are used to estimate them. The first approach to estimate these quantities is the method of maximum likelihood. Furthermore, and for the first time, we consider the method of maximum product of spacing to estimate the mentioned entropy measures. Also, a simulation study is carried out and two real data sets are analysed. The numerical outcomes showed that the maximum likelihood provides good point estimates while the interval estimates based on the maximum product of spacing method have the shortest confidence interval lengths.

Keywords

• Inverse Weibull distribution
• maximum likelihood estimation
• maximum product of spacing estimation
• Rényi entropy
• Shannon entropy