# PDc

PDc computes breakdown point and efficiency associated with tuning constant alpha for minimum power divergence estimator

## Syntax

• bdp=PDc(alpha)example
• [bdp,eff]=PDc(___)example

## Description

 bdp =PDc(alpha) PDc with just one output argument.

 [bdp, eff] =PDc(___) PDc with 2 output arguments.

## Examples

expand all

### PDc with just one output argument.

[bdp]=PDc(1)
disp('Break down point')
disp(bdp)

### PDc with 2 output arguments.

alpha=1;
[bdp,eff]=PDc(alpha)
disp('Break down point and efficienty')
disp(['alpha=' num2str(alpha)])
disp(['bdp=' num2str(bdp)])
disp(['eff=' num2str(eff)])

## Related Examples

expand all

### Breakdown point and efficiency.

Analysis of breakdown point and asymptotic efficiency at the normal distribution as a function of alpha in regression.

c=0.01:0.01:1;
[bdp,eff]=PDc(c);
subplot(2,1,1)
plot(c,bdp)
xlabel('$\alpha$','Interpreter','Latex','FontSize',16)
ylabel('Breakdown point','Interpreter','none')
subplot(2,1,2)
plot(c,eff)
xlabel('$\alpha$','Interpreter','Latex','FontSize',16)
ylabel('Asymptotic efficiency','Interpreter','none')

## Input Arguments

### alpha — tuning constant alpha. Scalar or Vector.

Scalar greater than 0 which controls the robustness/efficiency of the estimator

Data Types: single| double

## Output Arguments

### bdp —bdp. Scalar

Breakdown point associated to the supplied value of c

### eff —eff. Scalar

Efficiency associated to the supplied value of c Remark: if alpha is a vector bdp and eff will also be vectors with the same size of alpha. For example bdp(3) and eff(3) are associated to alpha(3) ....

Riani, M. Atkinson, A.C., Corbellini A. and Perrotta A. (2020), Robust Regression with Density Power Divergence: Theory, Comparisons and Data Analysis, submitted.