Bvar: (Sample) Variance
In SAFD: Statistical Analysis of Fuzzy Data

Description Usage Arguments Details Value Note Author(s) References See Also Examples

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 if each element of the list has the correct form and 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.

1	Bvar(XX, theta = 1/3)

`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`

See examples

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

In case you find (almost surely existing) bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses.

Wolfgang Trutschnig <wolfgang@trutschnig.net>, Asun Lubiano <lubiano@uniovi.es>

[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 as bertoluzza, Mmean

#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:
data(Trees)
Species1_Var<-Bvar(Trees$species1,1/3)
Species1_Var
Species2_Var<-Bvar(Trees$species2,1/3)
Species2_Var
Species3_Var<-Bvar(Trees$species3,1/3)
Species3_Var