Var function

Variance of a trapezoidal fuzzy sample

Given a sample of trapezoidal fuzzy numbers contained in a matrix F, the function calculates the variance of these numbers with respect to the mid/spr distance. The function first checks if the input matrix F is given in the correct form (tested by checkingTra).

Var(F, a = 1, b = 1, theta = 1/3)

Arguments

• F: matrix of dimension n x 4 containing n trapezoidal fuzzy numbers characterized by their four values inf0,inf1,sup1,sup0. The function implicitly checks if the matrix is in the correct form (tested by checkingTra).
• a: number >0, by default a=1. It is the first parameter of a beta distribution which corresponds to a weighting measure on [0,1].
• b: number >0, by default b=1. It is the second parameter of a beta distribution which corresponds to a weighting measure on [0,1].
• theta: number >0, by default theta=1/3. It is the weight of the spread in the mid/spr distance.

Details

See examples

Returns

The function returns the variance of the sample with respect to the mid/spr distance, which is a real number.

References

[1] De la Rosa de Saa, S.; Lubiano M.A.; Sinova, B.; Filzmoser, P.: Robust scale estimators for fuzzy data, Advances in Data Analysis and Classification, pp. 1-28 (2015)

Author(s)

Asun Lubiano lubiano@uniovi.es, Sara de la Rosa de Saa rosasara@uniovi.es

Note

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

See Also

checkingTra, Mean, DthetaphiTra

Examples

# Example 1:
F=SimulCASE1(10)
Var(F,1,1,1)

# Example 2:
F=matrix(c(1,0,2,3),nrow=1)
Var(F)