FUZZY EMPIRICAL DISTRIBUTION FUNCTION: PROPERTIES AND APPLICATION

被引：0

作者：

Hesamian, Gholamreza ^{[1
]}

Taheri, S. M. ^{[2
,3
]}

机构：

[1] Payame Noor Univ, Dept Stat, Tehran 193953697, Iran

[2] Univ Tehran, Coll Engn, Dept Engn Sci, Tehran, Iran

[3] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

来源：

KYBERNETIKA | 2013年 / 49卷 / 06期

关键词：

fuzzy cumulative distribution function; fuzzy empirical distribution function; Kolmogorov-Smirnov test; fuzzy p-value; convergence with probability one; degree of accept; degree of reject; Glivenko-Cantelli theorem; RANDOM-VARIABLES; VAGUE DATA; TESTS; HYPOTHESES; NUMBERS; STATISTICS;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The concepts of cumulative distribution function and empirical distribution function are investigated for fuzzy random variables. Some limit theorems related to such functions are established. As an application of the obtained results, a method of handling fuzziness upon the usual method of Kolmogorov-Smirnov one-sample test is proposed. We transact the a-level set of imprecise observations in order to extend the usual method of Kolmogorov-Smirnov one-sample test. To do this, the concepts of fuzzy Kolmogorov-Smirnov one-sample test statistic and p-value are extended to the fuzzy Kolmogorov-Smirnov one-sample test statistic and fuzzy p-value, respectively. Finally, a preference degree between two fuzzy numbers is employed for comparing the observed fuzzy p-value and the given fuzzy significance level, in order to accept or reject the null hypothesis of interest. Some numerical examples are provided to clarify the discussions in this paper.

引用

页码：962 / 982

页数：21

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