# M.estimate: M-estimator of scale of a trapezoidal fuzzy sample In FuzzyStatTra: Statistical Methods for Trapezoidal Fuzzy Numbers

## Description

This function calculates the M-estimator of scale with loss function given in M for a matrix of trapezoidal fuzzy numbers F. For computing the M-estimator, a method called “iterative reweighting” is used. The employed metric in the M-equation can be the 1-norm distance, the mid/spr distance or the (\varphi,θ)-wabl/ldev/rdev distance. The function first checks if the input matrix F is given in the correct form (tested by checkingTra).

## Usage

 1 M.estimate(F, M, est_initial, delta, epsilon, type, 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). M name of the loss function. It can be “Huber”, “Tukey” or “Cauchy”. est_initial initial scale estimate. delta number in (0,1). It is present in the M-equation. epsilon number >0. It is the tolerance allowed in the algorithm. type number 1, 2 or 3: if type==1, the 1-norm distance will be considered in the calculation of the M-estimator. If type==2, the mid/spr distance will be considered. By contrast, if type==3, the (\varphi,θ)-wabl/ldev/rdev distance will be used. 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] in the mid/spr distance or in the (\varphi,θ)-wabl/ldev/rdev distance. 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] in the mid/spr distance or in the (\varphi,θ)-wabl/ldev/rdev distance. theta number >0, by default theta=1/3. It is the weight of the spread in the mid/spr distance and the weight of the ldev and rdev in the (\varphi,θ)-wabl/ldev/rdev distance.

See examples

## Value

The function returns the value of the M-estimator of scale, 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>

checkingTra, Rho1Tra, DthetaphiTra, DwablphiTra
 1 2 3 4 5 6 7 # Example 1: F=SimulCASE1(100) U=Median1norm(F) est_initial=MDD(F,U,1) delta=0.5 epsilon=10^(-5) M.estimate(F,"Huber",est_initial,delta,epsilon,1)