A test for fuzzy exponentiality based on Kullback-Leibler information

Article type: Research Article

Authors: Kong, Lingtao^{; *}

Affiliations: School of Statistics, Shandong University of Finance and Economics, Jinan, China

Correspondence: [*] Corresponding author. Lingtao Kong. E-mail: kltgw80@163.com.

Abstract: The exponential distribution has been widely used in engineering, social and biological sciences. In this paper, we propose a new goodness-of-fit test for fuzzy exponentiality using α-pessimistic value. The test statistics is established based on Kullback-Leibler information. By using Monte Carlo method, we obtain the empirical critical points of the test statistic at four different significant levels. To evaluate the performance of the proposed test, we compare it with four commonly used tests through some simulations. Experimental studies show that the proposed test has higher power than other tests in most cases. In particular, for the uniform and linear failure rate alternatives, our method has the best performance. A real data example is investigated to show the application of our test.

Keywords: Triangular fuzzy number, α-pessimistic value, power, Kullback-Leibler information

DOI: 10.3233/JIFS-202555

Journal: Journal of Intelligent & Fuzzy Systems, vol. 42, no. 3, pp. 1281-1288, 2022