# PDpsider

PDpsider computes derivative of psi function (second derivative of rho function) for minimum power divergence estimator

## Syntax

• psider=PDpsider(u,alpha)example

## Description

 psider =PDpsider(u, alpha) Plot the second derivative of minimum power divergence estimator.

## Examples

expand all

### Plot the second derivative of minimum power divergence estimator.

x=-6:0.01:6;
alpha=1;
c=2;
psiPDder=PDpsider(x,c);
plot(x,psiPDder)
xlabel('x','Interpreter','Latex')
ylabel('$\psi''(x)$','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

### psider —derivative of psi function.  Vector

n x 1 vector which contains the values of the derivative of the psi function of minimum power divergence estimator associated to the residuals or Mahalanobis distances for the n units of the sample.

Function PDpsider transforms vector u as follows $PDpsider(u)= \alpha (1- \alpha u^2) \exp{-\alpha u^2/2}$