On Entropy Estimation of Inverse Weibull Distribution under Improved Adaptive Progressively Type-II Censoring with Applications

Abstract

This article utilizes improved adaptive progressively Type-II censored data to estimate the entropy of the inverse Weibull distribution. Rényi, q, and Shannon entropy measurements are used to define entropy to achieve this objective. Both point and interval estimations of the entropy quantities are investigated through the maximum likelihood and maximum product of spacing methods. Two parametric bootstrap confidence intervals based on the two estimation techniques are also considered for the various entropy measures. A Monte Carlo simulation study is conducted to investigate how estimates behave at various sample sizes and different censoring schemes based on some statistical measurements. The simulations demonstrate that, as anticipated, when the sample size grows, the estimation accuracy also grows. Furthermore, they show that the estimated entropy measures get closer to the actual entropy values when the censoring level decreases. For purposes of explanation, two applications to actual datasets are taken into consideration. The results verified that the adaptive or improved adaptive progressive censoring schemes give more information about data than the conventional progressive censoring scheme in terms of minimum entropy measures.

Keywords

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