Thread Subject:

gevfit, how to estimate paramters of a distribution when know probability distribution values of a random variable

Hi everyone,
I have a problem in using command gevfit, Parmhat = gevfit(X), where X is the sample data of a distribution. What I have is the sample points x(such as -20:20) and corresponding probability distribution values y, and find both gevfit(y) and gevfit(x) will not get the right parameters. So, what is my main problem in using gevfit? Or deduce the new expression from the definition of gev function? Any suggestions are greatly appreciated.

clear;clc;dbstop if error;
x=linspace(-20,20,1000);
k=0.5;mu=1;sigma=0;
y=pdf('gev',x,k,mu,sigma);
xquantile=icdf('gev',0.95,k,mu,sigma); %% calculate the quantile point of 0.95,that is x meeting P(X<=x)=0.95;
x2=2*xquantile-x; %% make x=xquantile as symmetry axis;
id1=x<=xquantile;id1=fliplr(id1);
id2=x>xquantile;id2=fliplr(id2);
y2=[y(id2) y(id1)]; %% x2 and y2 is the locations of new curve.
figure(1);clf;
plot(x,y,'-',x2,y2,'-*');
parasf=gevfit(y2);
y3=pdf('gev',y2,parasf(1),parasf(2),parasf(3));
plot(x2,y3,'-d');hold off;

lily, it sounds like maybe you are fitting a curve, not fitting a
distribution. See if this

<http://www.mathworks.com/products/statistics/examples.html?file=/products/demos/shipping/stats/cfitdfitdemo.html>

is of any help.

If you really are fitting a distribution, not a curve, and what you have
is in effect a histogram of values drawn from a distribution, and you
don't have access to the raw data, then gevfit isn't what you need.
What you can do is to define your own custom distribution that is a
"binned" version of the GEV, and use MLE to fit using that. But if you
have the raw data, you should use those.


On 8/9/2012 11:48 PM, lily wrote:
> Hi everyone,
> I have a problem in using command gevfit, Parmhat = gevfit(X), where X
> is the sample data of a distribution. What I have is the sample points
> x(such as -20:20) and corresponding probability distribution values y,
> and find both gevfit(y) and gevfit(x) will not get the right parameters.
> So, what is my main problem in using gevfit? Or deduce the new
> expression from the definition of gev function? Any suggestions are
> greatly appreciated.
>
> clear;clc;dbstop if error;
> x=linspace(-20,20,1000);
> k=0.5;mu=1;sigma=0;
> y=pdf('gev',x,k,mu,sigma);
> xquantile=icdf('gev',0.95,k,mu,sigma); %% calculate the quantile point
> of 0.95,that is x meeting P(X<=x)=0.95;
> x2=2*xquantile-x; %% make x=xquantile as symmetry
> axis;
> id1=x<=xquantile;id1=fliplr(id1);
> id2=x>xquantile;id2=fliplr(id2);
> y2=[y(id2) y(id1)]; %% x2 and y2 is the locations of
> new curve.
> figure(1);clf;
> plot(x,y,'-',x2,y2,'-*');
> parasf=gevfit(y2);
> y3=pdf('gev',y2,parasf(1),parasf(2),parasf(3));
> plot(x2,y3,'-d');hold off;