SAFD (version 0.02)

Bcov: (Sample) Covariance

Description

The sample covariance of two samples of polygonal fuzzy numbers with respect to the Bertoluzza distance is calculated. Given lists XX, YY of polygonal fuzzy numbers the functions first checks (1) if each element of the two lists is in the correct form (tested by checking), (2) if the alpha-levels of all elements in the two lists coincide and (3) if the lists have the same length. If all conditions are fulfilled the Bertoluzza covariance will be returned. If not, NA will be returned - in this case the translator function can be used to transform the elements of the lists 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

Bcov(XX, YY, theta = 1/3)

Arguments

XX

...list of polygonal fuzzy numbers (the functions implicitly checks the conditions) having the same length as YY

YY

...list of polygonal fuzzy numbers (the functions implicitly checks the conditions) having the same length as XX

theta

...numeric and >0, see bertoluzza

Value

• Given input XX, YY in the correct format the function returns the Bertoluzza covariance of the samples XX, YY.

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 checking, Mmean, lrmodel, Bcor, Bvar

Examples

#Example 1:
data(XX)
V<-translator(XX[[3]],100)
XX<-list(length=10)
YY<-XX
  for(i in 1:10){
   XX[[i]]<-generator(V,,,)
   YY[[i]]<-XX[[i]]
   YY[[i]]$x<-5*YY[[i]]$x+1
   }
Bcov(XX,YY,1/3)

#Example 2:
data(XX)
V<-translator(XX[[3]],51)
XX<-list(length=500)
YY<-XX
  for(i in 1:500){
   XX[[i]]<-generator(V,,,)
   YY[[i]]<-XX[[i]]
   YY[[i]]$x<-5*YY[[i]]$x+1
   }
Bcov(XX,YY,1/3)
Bcor(XX,YY,1/3)