# HAbdp

HAbdp finds the constant c associated to the supplied breakdown point

## Syntax

• ctun=HAbdp(bdp,p)example
• ctun=HAbdp(bdp,p,abc)example

## Description

 ctun =HAbdp(bdp, p) Find constant c for bdp=0.5.

 ctun =HAbdp(bdp, p, abc) Find constant c for bdp=0.5 when abc=[1.5 3.5 8].

## Examples

expand all

### Find constant c for bdp=0.5.

The constant c associated to a breakdown point of 50 per cent in regression is 0.198131771596856

c=HAbdp(0.5,1);
disp(c);
    0.1981



### Find constant c for bdp=0.5 when abc=[1.5 3.5 8].

The constant c associated to a breakdown point of 50 per cent in regression is

c=HAbdp(0.5,1,[1.5 3.5 8]);
disp(c);
    0.2119



## Input Arguments

### bdp — breakdown point. Scalar.

Scalar defining breakdown point (i.e a number between 0 and 0.5)

Data Types: single|double

### p — number of response variables. Scalar.

e.g. in regression p=1

Data Types: single|double|int32|int64

### abc — parameters of Hampel estimator. Vector.

Vector of length 3 which contains the parameters of Hampel estimator. If vector abc is not specified it is set equal to [2, 4, 8]

Example: [1.5,3.5,8] 

Data Types: double

## Output Arguments

### ctun —Requested tuning constant. Scalar

Tuning constatnt of Hampel rho function associated to requested breakdown point

Function HApsi transforms vector u as follows.

$HApsi(u) = \left\{ \begin{array}{cc} u & |u| <= a \\ a \times sign(u) & a <= |u| < b \\ a \frac{c-|u|}{c-b} \times sign(u) & b <= |u| < c \\ 0 & |u| >= c \end{array} \right.$

where $a$= ctun *param(1).

$b$= ctun *param(2).

$c$= ctun *param(3).

The default is $a$= 2*ctun.

$b$= 4*ctun.

$c$= 8*ctun.

It is necessary to have 0 <= a <= b <= c

Hoaglin, D.C., Mosteller, F., Tukey, J.W. (1982), "Understanding Robust and Exploratory Data Analysis", Wiley, New York.