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# kdedemo2

## PURPOSE

Demonstrate the difference between transformation- and ordinary-KDE

## SYNOPSIS

This is a script file.

## DESCRIPTION

``` KDEDEMO2 Demonstrate the difference between transformation- and ordinary-KDE

KDEDEMO2 shows that the transformation KDE is a better estimate for
Rayleigh distributed data around 0 than the ordinary KDE.```

## CROSS-REFERENCE INFORMATION

This function calls:
 kde Kernel Density Estimator. kdeoptset Create or alter KDE OPTIONS structure. pdfplot Plot contents of pdf structures wraylpdf Rayleigh probability density function wraylrnd Random matrices from a Rayleigh distribution
This function is called by:

## SOURCE CODE

```001 %KDEDEMO2 Demonstrate the difference between transformation- and ordinary-KDE
002 %
003 % KDEDEMO2 shows that the transformation KDE is a better estimate for
004 % Rayleigh distributed data around 0 than the ordinary KDE.
005
006 %%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*- Mode: Matlab -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%
007 %% kdedemo2.m ---
008 %% Author          : Per Andreas Brodtkorb
009 %% Created On      : Fri Nov 19 13:29:53 2004
012 %% Update Count    : 20
013 %% Status          : Unknown, Use with caution!
014 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
015
016 data = wraylrnd(1,300,1);
017
018 x = linspace(sqrt(eps),5,55);
019
020 f = kde(data);
021 pdfplot(f)
022 title('Ordinary KDE')
023 hold on
024 plot(x,wraylpdf(x,1),':')
025 hold off
026
027 %wnormplot((data).^(L2)) % gives a straight line => L2 = 0.5 reasonable
028
029 kopt = kdeoptset('L2',0.5);
030
031 f1 = kde(data,kopt,x);
032 figure(gcf+1)
033 pdfplot(f1)
034 title('Transformation KDE')
035 hold on
036 plot(x,wraylpdf(x,1),':')
037 hold off
038 figure(gcf-1)```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

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