Fitting a double exponential cumulative distribution function
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Hello,
I have an empirical probability distribution function (PDF) that fits best to a double exponential, i.e. by specifying exp2 in the fit function:
a*exp(b*x) + c*exp(d*x)
However, I want to ensure that this is also true without binning, so I want to use an exponential cumulative distribution function (CDF).
So, I construct a CDF like this:
[p,x]=ecdf(x);
Now I want to fit a double CDF to this. For fitting to a double CDF, it seems like I could fit the double CDF with cftool, but I'd rather use the fit function as it needs to be automated. So does anyone know a) if I can specify a custom equation with the fit function and b) what the equation for a double exponential CDF would look like?
Thank you!
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Tom Lane
le 22 Mar 2012
You can do most things like this by writing a pdf and calling mle:
>> x = [exprnd(1,1000,1); exprnd(5,2000,1)];
>> pdf = @(x,p,a,b) (p)*exppdf(x,a) + (1-p)*exppdf(x,b)
>> mle(x,'pdf',pdf,'start',[.5,2,3])
ans =
0.31645 0.96406 4.8809
I was lucky that I got an estimate satisfying 0<p<1. If I didn't, I'd have to choose a parametrization to prevent that.
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Peter Perkins
le 22 Mar 2012
Grant, can I suggest that you take a look at
before going too much further? It may be that you want dfittool, not cftool.
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