Neutrosophic entropy measures for the Weibull distribution: theory and applications

Rehan Ahmad Khan Sherwani,Tooba Arshad,Mohammed Albassam,Muhammad Aslam,Shumaila Abbas

doi:10.1007/s40747-021-00501-y

Rehan Ahmad Khan Sherwani, Tooba Arshad + Show 3 more

Open Access

https://doi.org/10.1007/s40747-021-00501-y

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Abstract

Entropy is a standard measure used to determine the uncertainty, randomness, or chaos of experimental outcomes and is quite popular in statistical distribution theory. Entropy methods available in the literature quantify the information of a random variable with exact numbers and lacks in dealing with the interval value data. An indeterminate state of an experiment generally generates the data in interval form. The indeterminacy property of interval-valued data makes it a neutrosophic form data. This research proposed some modified forms of entropy measures for an important lifetime distribution called Weibull distribution by considering the neutrosophic form of the data. The performance of the proposed methods is assessed via a simulation study and three real-life data applications. The simulation and real-life data examples suggested that the proposed methodologies of entropies for the Weibull distribution are more suitable when the random variable of the distribution is in an interval form and has indeterminacy or vagueness in it.

Highlights

The field of information theory quantifies the information of an event by considering the concept of the extent of surprise that underlies an event
Entropy is an essential measure from information theory to determine the vagueness of a data set in an exact form
This research fills the gap by setting the entropy measures in distribution theory in the context of neutrosophy and interval-valued data

Summary

Introduction

The field of information theory quantifies the information of an event by considering the concept of the extent of surprise that underlies an event. Using this Eq (8), the neutrosophic Shannon entropy of Weibull distribution is distribution is obtained from the upper bound, among which lies the uncertainty in the sample. 6. The empirical neutrosophic Shannon and Rényi entropy for Weibull distribution were computed by taking the average of the obtained matrix of the obtained entropies in the interval form.

Results

Conclusion