Affiliations: Department of Statistics, Payame Noor University, Tehran, Iran | Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran
Note: [] Corresponding author. Jalal Chachi, Department of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran. Tel./Fax: +98 231 3354059; E-mails: [email protected] (J. Chachi), [email protected] (G. Hesamian).
Abstract: This paper extends the non-parametric Sign test to the case when available observations and underlying hypotheses about the population median are imprecise quantities. To do this, by using some elements of possibility theory, we suggest a ranking index among imprecise observations. The index is applied to extend the usual concepts of classical hypothesis testing problem to obtain Sing test statistic and interval p-value. Comparing p-value and a nominal significance level, the fuzzy non-parametric Sign test is constructed providing some degrees to accept or reject the imprecise hypotheses. Several numerical examples are provided throughout the paper to clarify the proposed approach. Finally, a comprehensive review of several well-known non-parametric test approaches is given.
Keywords: Fuzzy sign test, imprecise hypotheses, imprecise observations, interval p-value, necessity and possibility indices
