# probability density function normalization

조회 수: 35(최근 30일)
Tamara Szecsey 10 Mar 2021
댓글: Tamara Szecsey 11 Mar 2021
I would like to illustrate the probability density function and the histogram of a data set. This is the code I used so far:
clc;
xValues = 0:0.001:0.5;
for i = [21,24]
figure;
grid on;
hold on;
% newcolors = [0 0 0; 1 0 0; 0.3010 0.7450 0.9330; 0.9290 0.6940 0.1250];
% colororder(newcolors);
for j = 0:c:(3*c) %alle 3 Messarten vergleichen
% histfit(T_mean{i+j},20,'kernel')
histogram(T_mean{i+j},20,'Normalization','pdf','DisplayStyle','stairs');
pd = fitdist(T_mean{i+j},'Kernel');
y = pdf(pd,xValues);
plot(xValues,y)
% ksdensity(T_mean{i+j})
end
hold off;
end
where c is 24. The T_mean is a table composed of 4 tables with length of 24, which are 24 different sets of data. In this case I only need 21 and 24, which each contain a vector. With this code, the probability density function and the histogram have the same normalization. But the y-axis is do large. The area under the pdf should be smaller than 1, so the y-axis could be read in %. Perhaps I don't understand the pdf function correctly. Here is a picture of one of the graph outputs:
The pdf seems to have different definitions in Matlab:
and
Matlab seems to use the second one in this case.
How can I normalize the histogram as 'probability' but also normalize the pdf the same way?

댓글을 달려면 로그인하십시오.

### 채택된 답변

Jeff Miller 10 Mar 2021
The pdf values are defined so that the total area under the pdf curve equals 1, but these values will exceed 1 (and, hence, not look like probabilities) when the range of X is less than one unit. To make pdf values look more like probabilities, you can adjust for that roughly like this:
% Generate some example values that look a little like yours:
mu = 0.25;
sigma = 0.1;
data = randn(500,1)*sigma + mu;
range = max(data) - min(data);
figure;
hold on;
nbins = 20; % for the histogram
histogram(data,nbins,'Normalization','probability','DisplayStyle','stairs');
pd = fitdist(data,'Kernel');
xValues = 0:0.001:0.5; % for computing the pdf
y = pdf(pd,xValues) / nbins * range; % adjust to match probability based on nbins & range
plot(xValues,y)
##### 댓글 수: 3표시숨기기 이전 댓글 수: 2
Tamara Szecsey 11 Mar 2021
Now I understand, thank you.

댓글을 달려면 로그인하십시오.

R2020b

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by