# Estimate an expression for a Probability Density Function

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john birt on 23 Feb 2011
I have a 5 parameter distribution, I have estimates of all five parameters. I also have the characteristic function, moment generating function and the cumulant function for the distribution.
What I dont have is an expression for the probability density function of the distribution. (I wish to plot the prob density function)
Knowing what Ive I know, can matlab estimate the probability density function?

Matt Tearle on 23 Feb 2011
By the "cumulant" function, do you mean the cumulative probability density? Because, in that case, the PDF is just the derivative of the CDF. If you can't get the derivative analytically (or it's just too messy to bother with), use diff to approximate it
x = linespace(-20:0.1:20);
mycdf = ...(x)...
mypdf = diff(mycdf)./diff(x);
john birt on 23 Feb 2011
No, by the cumulant function I mean the c.g.f or cumulant generating function which is used for generating the cumulants of the distribution. The c.g.f is just the log of the characteristic function.
I do not have the CDF or the PDF but which to numically estimate them from my five parameters, I also have the characteristic function and the moment generating function.