Thread Subject: cdf of mixture distributions?

hello all,

is there a generic way to compute the cdf of bimodal distributions,
say, a mixture of gaussians in matlab? example: p*normpdf(10, 5) + (1-
p)*normpdf(10, 6). how can i get the cdf of this result, aside from
brute force binning and summing?

thank yous.

perfreem@gmail.com wrote in message <6d5ff2bf-cf4a-4163-a293-5dcad79478ed@v56g2000hsf.googlegroups.com>...
> hello all,
>
> is there a generic way to compute the cdf of bimodal distributions,
> say, a mixture of gaussians in matlab? example: p*normpdf(10, 5) + (1-
> p)*normpdf(10, 6). how can i get the cdf of this result, aside from
> brute force binning and summing?
>
> thank yous.


For Gaussian mixtures, you can use erf()

perfreem@gmail.com wrote:
> hello all,
>
> is there a generic way to compute the cdf of bimodal distributions,
> say, a mixture of gaussians in matlab? example: p*normpdf(10, 5) + (1-
> p)*normpdf(10, 6). how can i get the cdf of this result, aside from
> brute force binning and summing?

It's the same idea, right? If your mixture has two components, N(5,1) and N(6,1) (your example), with mixing probs [p 1-p], then the PDF at 10 is p*normpdf(10,5) + (1-p)*normpdf(10,6) and the CDF is p*normcdf(10,5) + (1-p)*normcdf(10,6).

Here's maybe a more interesting example:

xx = linspace(0,10,1000);
yy = .2*normcdf(xx,3) + (1-.2)*normcdf(xx,7);
plot(xx,yy);

Hope this helps.

perfreem@gmail.com wrote:
> hello all,
>
> is there a generic way to compute the cdf of bimodal distributions,
> say, a mixture of gaussians in matlab? example: p*normpdf(10, 5) + (1-
> p)*normpdf(10, 6). how can i get the cdf of this result, aside from
> brute force binning and summing?
>
> thank yous.

The statistical toolbox in Matlab supports computing CDF for mixture of
Gaussian. See GMDISTRIBUTION and GMDISTRIBUTION/CDF.

-Ting Su
Mathworks