how to get Gamma pdf from gamma cdf?

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Genhou 2014-1-16

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评论： Genhou 2014-1-24

Hello, everybody.

My question is this. i have a gamma cdf( cumulative distribution function) and corresponding x, now i want to get gamma pdf( probability distribution function) from the cdf data.

I have a the cdf and the corresponding x. such as:

 peak     10%     30%     50%    70%   90% ///                
 49        17     42      64     91    136 ///                 
 53        18     45      69     97    145

the first row is the cdf,this second and third row are the corresponding x, in meters.

I need get probability from 0 to 135m the step can be set 5 meter at interval.

How can I do this? thanks.

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the cyclist 2014-1-16

John, your comment confuses me, and I hope you can help me understand. He has values of x, and the corresponding cumulative percentages at those x values. Isn't that a CDF (albeit a very sparse and empirical one)? I trust your expertise enough to believe that there is a nuance here, but I don't see it.

John D'Errico 2014-1-16

No. That is NOT a CDF. A CDF is a Cumulative Distribution Function. A list of points FROM any function is not the function itself, but just a list of points. You may choose to interpolate those points, so getting a function that you may interpret as an empirical approximation to the CDF you so desire. But so far, all we have seen are a list of points from some function, without any information as to the source of those values. Unless you know the parameters of the Gamma CDF that putatively would produce these points, you don't have the true CDF.

An issue is that if all we have are a set of points that the poster CLAIMS represent points from a gamma CDF, then we don't really know that they do arise from any gamma CDF at all. For example, I can provide a set of points representing a distribution that is clearly bimodal, but claim that it "is" a Normal CDF. I'd be wrong of course.

So the problem seems most likely to do a distribution fit, trying to find the most reasonable Gamma distribution to match that list of points. There are tools for this in the stats TB.

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Answer 1

the cyclist 2014-1-16

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编辑：the cyclist 2014-1-16

I think the page http://www.mathworks.com/help/stats/examples/fitting-a-univariate-distribution-using-cumulative-probabilities.html explains the approach you could take. You'll probably want to read the whole page, but the most relevant part is probably the section entitled "Non-Location-Scale Families", where gamma fitting is discussed explicitly.