# PDpsix

PDpsix computes psi function (derivative of rho function) times x for minimum density power divergence estimator

## Syntax

• psix=PDpsix(u,alpha)example

## Description

 psix =PDpsix(u, alpha) Plot of psi function (derivative of rho function) times x for minimum density power divergence estimator.

## Examples

expand all

### Plot of psi function (derivative of rho function) times x for minimum density power divergence estimator.

x=-6:0.01:6;
psixPD=PDpsix(x,1);
plot(x,psixPD)
xlabel('x','Interpreter','Latex')
ylabel('$\psi_\alpha (x)$','Interpreter','Latex')

## Input Arguments

### u — scaled residuals or Mahalanobis distances. Vector.

n x 1 vector containing residuals or Mahalanobis distances for the n units of the sample

Data Types: single| double

### alpha — tuning parameter. Scalar.

Scalar in the interval (0,1] which controls the robustness/efficiency of the estimator (beta in regression or mu in the location case ...). The greater is alpha the greater is the bdp and smaller is the efficiency.

Data Types: single| double

## Output Arguments

### psix —Values of PD psi(u)*u function associated to the residuals or Mahalanobis distances for the n units of the sample. n -by- 1 vector

Function PDpsix transforms vector u as follows $PDpsix(u,alpha)= \alpha u^2 \exp(-\alpha (u^2/2));$