File:Kernel density estimation, comparison between rule of thumb and solve-the-equation bandwidth.png
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Summary
| Description | |
| Date | |
| Source |
 This diagram was created with MATLAB. |
| Author | Kernel estimator |
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The Matlab script for this example uses kde.m and is given below.
% Data
randn('seed',1) % Used for reproducibility
data = [randn(100,1)-10; randn(100,1)+10]; % Two Normals mixed
% True
phi = @(x) exp(-.5*x.^2)/sqrt(2*pi); % Normal Density
tpdf = @(x) phi(x+10)/2+phi(x-10)/2; % True Density
% Kernel
h = std(data)*(4/3/numel(data))^(1/5); % Bandwidth estimated by Silverman's Rule of Thumb
kernel = @(x) mean(phi((x-data)/h)/h); % Kernel Density
kpdf = @(x) arrayfun(kernel,x); % Elementwise application
% Plot
figure(2), clf, hold on
x = linspace(-25,+25,1000); % Linear Space
plot(x,tpdf(x)) % Plot True Density
plot(x,kpdf(x)) % Plot Kernel Density with Silverman's Rule of Thumb
kde(data) % Plot Kernel Density with Solve-the-Equation Bandwidth
#The same code with R language
#` Data
set.seed(1) #Used for reproducibility
data = c(rnorm(100,-10,1),rnorm(100,10,1)) #Two Normals mixed
#` True
phi = function(x) exp(-.5*x^2)/sqrt(2*pi) #Normal Density
tpdf = function(x) phi(x+10)/2+phi(x-10)/2 #True Density
#` Kernel
h = sd(data)*(4/3/length(data))^(1/5) #Bandwidth estimated by Silverman's Rule of Thumb
Kernel2 = function(x) mean(phi((x-data)/h)/h) #Kernel Density
kpdf = function(x) sapply(x,Kernel2) #Elementwise application
#` Plot
x=seq(-25,25,length=1000) #Linear Space
plot(x,tpdf(x),type="l",ylim=c(0,0.23),col="red") #Plot True Density
par(new=T)
plot(x,kpdf(x),type="l",ylim=c(0,0.23),xlab="",ylab="",axes=F) #Plot Kernel Density with Silverman's Rule of Thumb
Licensing
User:Kernel estimator, the copyright holder of this work, hereby publishes it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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Original upload log
Transferred from en.wikipedia to Commons using For the Common Good.
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 15:47, 19 April 2016 | 733 × 561 (28,809 bytes) | w:en:Kernel estimator (talk | contribs) | author: kernel estimator source: created by kernel estimator using the Matlab code on Wikipedia URL: N/A |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:39, 26 October 2018 | | 733 × 561 (28 KB) | wikimediacommons>Jumpow | Transferred from en.wikipedia: see original upload log above |
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