Bootstrap Approach to the One-Sample and Two- Sample Test of Variances of a Fuzzy Random Variable
The aim of this paper is to present in a concise and integrated way of the bootstrap approach to statistical testing of hypotheses about the variance of fuzzy random variable. In this approach, first a notion of fuzzy random variables is recalled. Then, we will consider hypothesis-tests for the (crisp-valued) variance of fuzzy data in a population. For this purpose, the $\alpha$-pessimistic values of the imprecise observations are used for defining a new notion of distance measure between fuzzy data, which is then used to make a procedure for testing the statistical hypotheses. Based on this argument, the application of bootstrap techniques in dealing with these testing problems will be introduced. The procedure develops a non-parametric approach to testing statistical hypotheses based on one-sample and two-sample fuzzy data.
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