the average of multiple Probability density functions
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Hallo,
I have a cell array of {1000,1} pds, they are all the same distribution, but they differ slightly in the parameter values
Does any one know how to get the average of these pds? I have got them in iterative process and would like now to know the mean or average of them
I though of taking the mean of the parameter values in the pds in for loop but I am truggling with the right way to do it because I keep getting errors.
it would be helpful if some one gives me a hint :)
I have attached the cell array (Temp) in mat file
Thanks in advanced!
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Image Analyst
2019년 12월 5일
J, it should work regardless of what toolboxes you have
s=load('temp.mat')
cellArray = s.Temp
s =
struct with fields:
Temp: {1000×1 cell}
cellArray =
1000×1 cell array
{1×1 prob.GeneralizedParetoDistribution}
{1×1 prob.GeneralizedParetoDistribution}
{1×1 prob.GeneralizedParetoDistribution}
{1×1 prob.GeneralizedParetoDistribution}
etc.
Jeff Miller
2019년 12월 5일
What do you mean by "the average of the probability distributions"?
For example, suppose one distribution is normal(0,1) and another distribution is normal(10,2). Is the average normal(5,1.5)? Or is the average bimodal with one mode around 0 and another around 10? Or is the average distribution something else?
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Ridwan Alam
2019년 12월 5일
The idea of "average" is ill-defined for pdfs.
In your case, all the 1000 distridutions are generalized paretos. Your theta is fixed in all pdfs, so you can certainly take the average of the sigma's and the k's. But what meaning/significance those "averages" carry, you need to come up with that.
If you are looking for the average expected value, you can calculate the mean (expected value) for each pareto and then average those. mean = theta + (sigma/(1-k)). ref: https://en.wikipedia.org/wiki/Generalized_Pareto_distribution
Also, if you are looking for the overall distribution parameters, you can combine the input data [available in Temp{}.InputData.data] and use gppdf().
Hope this helps.
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Ridwan Alam
2019년 12월 6일
편집: Ridwan Alam
2019년 12월 6일
Rima, as I mentioned one approach could be to stack all the inputdata from all the pdfs.
allInputData=[];
for i = 1:length(Temp)
allInputData = [allInputData; Temp{i}.InputData.data];
end
% in your case, theta is fixed
newTheta = Temp{1}.theta;
paramhat = gpfit(allInputData-newTheta);
newK = paramhat(1);
newSigma = paramhat(2);
Hope this helps.
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