# 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 efficiency')
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) ....

## References

Riani, M. Atkinson, A.C., Corbellini A. and Perrotta A. (2020), Robust Regression with Density Power Divergence: Theory, Comparisons and Data Analysis, Entropy, Vol. 22, 399.