SAFD (version 0.3)

Bvar: (Sample) Variance

Description

The sample variance of a sample of polygonal fuzzy numbers with respect to the Bertoluzza distance is calculated. Given a list XX of polygonal fuzzy numbers the function first checks (1) if each element of the list is in the correct form (tested by checking) and (2) if the alpha-levels of all elements in the list coincide. If these conditions are fulfilled the Bertoluzza sample variance will be returned (i.e. the average Bertoluzza distance of the elements of XX to its mean). If not the translator function can be used to transform the elements of the list in the correct format. For details see [1] from below, and replace the kernel K with the expression induced by the Bertoluzza metric. The parameter theta has to fulfill theta>0.

Usage

Bvar(XX, theta = 1/3)

Arguments

XX

...should be a list of polygonal fuzzy numbers (the functions implicitly checks the conditions) verifying the above mentioned conditions

theta

...numeric and >0, see bertoluzza

Value

• Given input XXin the correct format the function returns the Bertoluzza variance of the sample XX.

Details

See examples

References

[1] 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)

See Also

See Also as bertoluzza, Mmean,Bcov, Bcor

Examples

#Example 1:
data(XX)
X<-translator(XX[[1]],50)
Y<-translator(XX[[2]],50)
Z<-translator(XX[[3]],50)
YY<-list(X,Y,Z)
A<-Bvar(YY,1)
A

#Example 2:
data(XX)
v<-Bvar(list(XX[[1]],XX[[1]]),1/3)
v

#Example 3:
X<-data.frame(cbind(x=c(-2,-0.75,-0.25,0.5,1),alpha=c(0.3,0,1,0,0.3)))
Y<-data.frame(cbind(x=c(-2,-0.75,-0.25,0.5,1),alpha=c(0,0.3,1,0,0.3)))
Z<-data.frame(cbind(x=c(-2,-0.75,-0.25,0.5,1),alpha=c(0,0.6,1,1,0)))
ZZ<-list(X,Y,Z)
v<-Bvar(ZZ,1)
v

#Example 4
data(XX)
A<-Bvar(XX,1)
A