Fuzzy empirical distribution function: Properties and application

Gholamreza Hesamian; S. M. Taheri

Kybernetika (2013)

  • Volume: 49, Issue: 6, page 962-982
  • ISSN: 0023-5954

Abstract

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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 α -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.

How to cite

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Hesamian, Gholamreza, and Taheri, S. M.. "Fuzzy empirical distribution function: Properties and application." Kybernetika 49.6 (2013): 962-982. <http://eudml.org/doc/260815>.

@article{Hesamian2013,
abstract = {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 $\alpha $-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.},
author = {Hesamian, Gholamreza, Taheri, S. M.},
journal = {Kybernetika},
keywords = {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; fuzzy cumulative distribution function; fuzzy empirical distribution function; Kolmogorov-Smirnov test; fuzzy -value; convergence with probability one; degree of accept; degree of reject; Glivenko-Cantelli theorem},
language = {eng},
number = {6},
pages = {962-982},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Fuzzy empirical distribution function: Properties and application},
url = {http://eudml.org/doc/260815},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Hesamian, Gholamreza
AU - Taheri, S. M.
TI - Fuzzy empirical distribution function: Properties and application
JO - Kybernetika
PY - 2013
PB - Institute of Information Theory and Automation AS CR
VL - 49
IS - 6
SP - 962
EP - 982
AB - 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 $\alpha $-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.
LA - eng
KW - 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; fuzzy cumulative distribution function; fuzzy empirical distribution function; Kolmogorov-Smirnov test; fuzzy -value; convergence with probability one; degree of accept; degree of reject; Glivenko-Cantelli theorem
UR - http://eudml.org/doc/260815
ER -

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