bimodal Gaussian distribution function

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PChoppala on 28 Sep 2012
Hi
Greetings. I have a simple problem and will appreciate your help.
I am trying to plot the bimodal Gaussian distribution. The space is [0:0.1:20] and there are two means in one dimension.
I expect to obtain two peaks (one is an image of course) at the means [6;14], however, that's not what I get. I think I am going wrong somewhere, but am unable to figure out.
Yeah, I neglected the covariance matrix and the normalization constant, because I am normalizing at the complete function in the next step.
My implementation is here
mu=[6;14];
space=[0:.1:20];
x=[space;space];
L=exp(-((x-repmat(mu,1,size(T,2)))'*(x-repmat(mu,1,size(T,2))))/2);
L=L/sum(sum(L));
mesh(space,space,L);
P

Tom Lane on 2 Oct 2012
One more try. Check this out:
mu=[6;14];
space=[0:.1:20];
x = repmat(space,201,1);
y = repmat(space',1,201);
L = .5 * (1/(2*pi)) * exp(-.5 * ((x-mu(1)).^2 + (y-mu(2)).^2)) ...
+ .5 * (1/(2*pi)) * exp(-.5 * ((x-mu(2)).^2 + (y-mu(1)).^2));
mesh(space,space,L);
This creates arrays of x/y values so that each (i,j) index defines a point in the 2D space. Then it computes a thing L that is a mixture of two bivariate normal distributions. Their means are mirror images.

1 Comment

PChoppala on 2 Oct 2012
Yeah, thanks a lot. This is what I wanted to do.

Tom Lane on 29 Sep 2012
Is this what you want?
F = (1/sqrt(2*pi)) * .5*(exp(-.5*(space-mu(1)).^2) + exp(-.5*(space-mu(2)).^2));
plot(space,F)

PChoppala on 1 Oct 2012
Hi
Sorry for the delay. No, that was not what I meant.
I wanted F to be a 2-D surface that can be plotted using mesh. P(mu(1)) would take the x-axis, and P(mu(2)) would take the y-axis.
What you gave plotted both P(mu(1)) and P(mu(2)) on one single space. I think I made my problem clear!
P
Tom Lane on 1 Oct 2012
This is still not completely clear to me.This:
p1 = (1/sqrt(2*pi)) * exp(-.5*(x(1,:)-mu(1)).^2);
p2 = (1/sqrt(2*pi)) * exp(-.5*(x(2,:)-mu(2)).^2);
L = p1'*p2;
gives you a density in two-dimensional space with a single mode. Your original question specified a bimodal distribution with "two means in one dimension."
PChoppala on 1 Oct 2012
Hmm, you are right. I think I framed the question wrong.
I meant that the dimension of the mean is a single number (one dimension) and so its pdf is a 1-d function. Its not that both means lie in one space.
I want a 2-d function, one for pdf of mu(1) along x-axis and another for pdf of mu(2) along y-axis.
Along the x-axis, we find 6 and 14. Similarly on y-axis.
So I suppose the pdf in the joint space should have two peaks, one at (6,14) and the other at (14,6).
Oh yeah, to make it more clear, if I have 3 means, the joint space of the resulting pdf 'F' has to be 3-d and so on.
I am looking for a Matlab implementation that can do this.
I am not sure whether this idea of two peaks is correct or not, but that was what I was told.
Cheers P