Maximum entropy based testing for fuzzy exponential random variable and its applications

The entropy-based goodness-of-fit tests have gained prominence due to their easiness and accuracy. In this paper, the goodness of fit test problem is developed for widely used Exponential distribution under imprecise conditions. To this aim, a novel concept called fuzzy differential entropy is introduced to measure the degree of uncertainty for fuzzy random variables. Then, the fuzzy empirical differential entropy proposed to estimate the new fuzzy information measure. We consider the Vasicek estimator of entropy and use the \(\alpha \) $\alpha$ -pessimistic approach to propose an entropy-based goodness of fit test for the fuzzy Exponential distribution. The practical applicability and superiority of the proposed test over other fuzzy goodness-of-fit tests were demonstrated through Monte Carlo simulation using a numerical example and two real-life applications.