Var: Variance of a trapezoidal fuzzy sample

In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

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.

Details

See examples

Value

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

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.

Author(s)

Asun Lubiano <[e-mail]>, Sara de la Rosa de Saa <[e-mail]>

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)

FuzzyStatTra documentation built on May 2, 2019, 10:59 a.m.