SAFD-package: Statistical Analysis of Fuzzy Data
Description
The aim of the package is to provide some basic functions for doing statistics with
one-dimensional Fuzzy Data (in the form of polygonal fuzzy numbers).Details
ll{
Package: SAFD
Type: Package
Version: 0.3
Date: 2011-05-04
License: GPL (>=2)
LazyLoad: yes
}
The aim of the package is to provide some basic functions for doing statistics with one dimensional Fuzzy Data (in the form of polygonal fuzzy numbers). In particular, the package contains functions for the basic operations on the class of fuzzy numbers (sum, scalar product, mean, Hukuhara difference, quantiles) as well as for calculating (Bertoluzza) distance, sample variance, sample covariance, sample correlation, and the Dempster-Shafer (levelwise) histogram. Moreover a function to simulate fuzzy random variables, bootstrap tests for the equality of means, and a function to do linear regression given trapezoidal fuzzy data is included.
Version 0.3 fixes some bugs of version 0.2 and includes an additional function to calculate quantiles of samples of polygonal fuzzy numbers.References
[1] Bertoluzza, C., Corral, N., Salas, A.: On a new class of distances between fuzzy numbers, Mathware Soft Comput., 2, pp:71-84 (1995)
[2] Colubi, A.: Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy- and real-valued data, Fuzzy Sets and Systems, 160(3), pp. 344-356 (2009)
[3] Gil, M.A., Lopez, M.T., Lubiano, M.A., Montenegro, M.: Regression and correlation analyses of a linear relation between random intervals, Test, 10(1), pp. 183-201 (2001)
[4] Gil, M.A.; Montenegro, M.; Gonzalez-Rodriguez, G.; Colubi, A.; Casals, R.: Bootstrap approach to the multi-sample test of means with imprecise data, Computational Statistics and Data Analysis, 51(1), pp. 148-162 (2006)
[5] Gonzalez-Rodriguez, G.; Blanco, A.; Colubi, A.; Lubiano, M.A.: Estimation of a simple linear regression model for fuzzy random variables, Fuzzy Sets and Systems, 160(3), pp. 357-370 (2009)
[6] Gonzalez-Rodriguez, G., Colubi, A., Trutschnig, W.: Simulation of fuzzy random variables, Information Sciences, 179(5), pp. 642-653 (2009)
[7] Montenegro, M., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable, Metrika, 59, pp. 31-49 (2004)
[8] Montenegro, M., Casals, M.R., Lubiano, M.A., Gil, M.A.: Two-sample hypothesis tests of means of a fuzzy random variable, Information Sciences, Vol. 133(1-2), pp. 89-100 (2001)
[9] Trutschnig, W., A strong consistency result for fuzzy relative frequencies interpreted as estimator for the fuzzy-valued probability, Fuzzy Sets and Systems, Vol. 159, nr 3, pp. 259-269 (2008)
[10] Trutschnig, W., Gonzalez-Rodriguez, G., Colubi, A.; Gil, M.A.: A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread, Information Sciences, 179(23), pp. 3964-3972 (2009)
[11] Viertl, R., Hareter, D.: Beschreibung und Analyse unscharfer Information: Statistische Methoden fuer unscharfe Daten, Springer Wien New York, 2006See Also
http://bellman.ciencias.uniovi.es/SMIRE/