How to plot PDF and CDF for a normal distribution in matlab

Question

I couldn't find a function in matlab that implement gets mean and standard deviation of normal distribution and plot its PDF and CDF.

I am afraid the two functions I have implemented bellow are missing something, since I get maximal value for pdfNormal which is greater than 1.

function plotNormPDF(u,s,color)
    mu = u; 
    sigma = s; 
    x = (mu - 5 * sigma) : (sigma / 100) : (mu + 5 * sigma); 
    pdfNormal = normpdf(x, mu, sigma);
    string = 'the maximal pdfNormal is';
    string = sprintf('%s :%d', string,max(pdfNormal));
    disp(string)
    plot(x, pdfNormal/max(pdfNormal),color); 
end

And for the CDF norm

function plotNormCDF(u,s,color)
    mu = u; 
    sigma = s; 
    x = (mu -  5*sigma) : (sigma / 100) : (mu + 5*sigma); 
    pdfNormal = normpdf(x, mu, sigma);
    plot(x,cumsum(pdfNormal)./max(cumsum(pdfNormal)),color)
end

Here is an example for using both:

plotNormCDF(0.2, 0.1,'r')
plotNormPDF(0.2, 0.1,'r')

enter image description here

It's fine if the maximal value of the pdf is greater than 1: the density under the curve needs to integrate to 1. Consider this: take a single point on the pdf and set its value to 1 million. The area under this point is still 0, and so the area under the pdf is unaffected. Alternatively, consider a uniform distribution on [0,.5]: to integrate to one, the pdf equals 2 everywhere in the support. For more, reference the following whuber comment and the links he provides: http://stats.stackexchange.com/questions/47714/how-to-explain-what-density-is-and-the-interpretation-of-the-curves-height-to-n — David Marx, Nov 30 '13 at 13:38
Also see http://stats.stackexchange.com/questions/4220/a-probability-distribution-value-exceeding-1-is-ok — Glen_b, Nov 30 '13 at 14:59
"unlike a probability, a probability density function can take on values greater than one" in the Wikipedia page that you refer to. — A. Donda, Nov 30 '13 at 15:10

score 5 · Answer 1 · answered Nov 30 '13 at 15:07

5

You don't need all that code, look how simpler it is:

mu = 0.2; sigma = 0.1;
x = linspace (mu-4*sigma, mu+4*sigma);
plot(x, normpdf (x,mu,sigma))
plot(x, normcdf (x,mu,sigma))

answered Nov 30 '13 at 15:07

juliohm

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+1 Just add a third argument to `linspace` to achieve finer sampling of the x axis – Luis Mendo Nov 30 '13 at 15:42
1

`linspace(mu-4*sigma, mu+4*sigma, 10000)` – 0x90 Sep 11 '16 at 01:23

score 3 · Accepted Answer · answered Nov 30 '13 at 15:02

Your function plotNormPDF is correct except that you should not divide by the maximum. As David Marx wrote, there is no upper constraint on the values that a probability density function can attain, only a constraint regarding its integral over the range of possible values.

function plotNormPDF(u,s,color)
mu = u;
sigma = s;
x = (mu - 5 * sigma) : (sigma / 100) : (mu + 5 * sigma);
pdfNormal = normpdf(x, mu, sigma);
string = 'the maximal pdfNormal is';
string = sprintf('%s :%d', string,max(pdfNormal));
disp(string)
plot(x, pdfNormal,color);
end

Your function plotNormCDF is correct in principle, but probably not very precise because it approximates an integral by a cumulative sum. Better to use the function normcdf. Normalization of the maximum to 1 here is neither necessary nor does it have an effect.

function plotNormCDF(u,s,color)
mu = u;
sigma = s;
x = (mu -  5*sigma) : (sigma / 100) : (mu + 5*sigma);
cdfNormal = normcdf(x, mu, sigma);
plot(x,cdfNormal,color)
end

How to plot PDF and CDF for a normal distribution in matlab

2 Answers2