Gaussian
distribution – how to plot it in Matlab

In statistics
and probability theory,
the Gaussian distribution
is a
continuous distribution that gives a good description of data that
cluster around a mean. The graph or plot of the associated probability
density has a peak at the mean, and is known as the Gaussian function
or bell curve.
The Probability Density Function (PDF) in this case can be defined as:

where
The formula
above can me coded in Matlab easily, like this:
function f =
gauss_distribution(x, mu, s)
p1 = .5
* ((x  mu)/s) .^ 2;
p2 = (s
* sqrt(2*pi));
f =
exp(p1) ./ p2;
Now,
let’s use it in an example.
We
produce 500 random numbers between 100 and 100, with mean m = 0 and
standard
deviation s
= 30. The code is:
a =
100; b = 100;
x = a +
(ba) * rand(1, 500);
m = (a +
b)/2;
s = 30;
Then,
we plot this information using our bell curve:
f
= gauss_distribution(x,
m, s);
plot(x,f,'.')
grid on
title('Bell
Curve')
xlabel('Randomly
produced numbers')
ylabel('Gauss
Distribution')
The
produced shape is:
An important property of
this bellshaped curve is that the values less
than one standard deviation from the mean (between green lines below)
represent
approximately 68.2%
of the area under the curve, while two standard
deviations
from the mean (between red lines below) take about 95.4%, and three
standard
deviations account for about 99.7% of the area.
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