Try to make a fitting for my data distribution

Dear ALL

I have a problem on the fitting for my data, let me explain:-

i have my data, i call it (y), y is matrix its size= 1 X 64809

The histogram for y is in this figure https://www.dropbox.com/s/i3d40aeegcb2had/1.jpg

I am looking for the best distribution by using dfittool ( i don't know whether this tool is good or not). So,this tool gives me that the best one is t location-scale with the parameters ( mu=0.000346043,sigma=0.00195851 and degree of freedom=0.882799),please see this figure https://www.dropbox.com/s/976xiawizx4qvma/2.jpg.

After all, i generat a random number matrix ( X ) with same size of y-matrix (size= 1 X 64809) and withe the same t location-scale parameters, by using the folowing functions:-

dist = ProbDistUnivParam('tlocationscale',[0.000346043,0.00195851,0.882799]);

X=random(dist,1,length(y)); % the random  number matrix

Now , to check whether my distribution is fitted my data or not, i used a qqplot fnction as

qqplot(X,y).

and i get this plot https://www.dropbox.com/s/on4z448bytayp0h/3.jpg

So, the question is, why the two distrbuation is not similar?? and why there is not matching?

please help me, and if any one need my data i can send him to help me on the fitting distribution.

Thanks in advance

[RAYYAN]

I am waiting for your help, please do me a favour.

[Frank]

Although I cannot access your picture attachments but I believe I encountered the same problem, could you tell me have you sorted this problem out? And how to sort it out?

Answer 1

[RAYYAN]

Dear ALL

I am waiting for your help.......

Answer 2

[Wayne King]

It looks to me like the problem you are seeing in the qqplot() is that your selection of the generalized t-distribution (t location-scale) results in a distribution with tails much wider than the vary narrow range of your Y data. For example, look at the PDF

   xval = -2:.01:2;
   y = pdf(ProbDistUnivParam('tlocationscale',[0.000346043,0.00195851,0.882799]),xval);
   plot(xval,y,'linewidth',2); set(gca,'ylim',[-0.5 max(y)]);

If you look at your random vector generated from this PDF, obviously the qqplot looks good

   L = 64809;
   X = random(dist,1,L);
   qqplot(X,dist)

but your actual data does not match the long-tailed behavior of the t location scale density even though the match in the center of the distribution is good.

The smaller the number of degrees of freedom in a t location-scale family PDF, the heavier the tails.

It's not that dfittool is not a good tool, it is a fine tool. It's just in this case either a different option would give a better fit, or perhaps a PDF not supported by dfittool.

[RAYYAN]

So, what do you recommend me to do?

Could you please help me, i can send you my data?

your response will be highly appreciated. thanks in advance