FuzzyStatTra (version 1.0)

Var:

Description

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).

Usage

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.

Value

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

Details

See examples

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)

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)