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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.

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)

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."

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