# 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

 1 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.

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 <lubiano@uniovi.es>, Sara de la Rosa de Saa <rosasara@uniovi.es>

## References

 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

 1 2 3 4 5 6 7 # 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.