how can i fit gumbel distribution to a dataset using only gevfit and setting shape parameter as zero. does this function estimate parameter based on mle?

how can i fit gumbel distribution to a dataset using only gevfit and setting shape parameter as zero. does this function estimate parameter based on mle? i don't want to use evfit as it does not directly compute the maximum value.

Answer 1

[Ayush]

Hi Payel,

I understand that you want to fit the Gumbel distribution to a dataset using only “gevfit” function, with shape parameter set to zero.

You can use the “evrnd” function to generate the numbers from a Gumbel distribution. Once you have generated the required data, pass it through the “gevfit” function. This will estimate the parameters of the Gumbel distribution using the (maximum likelihood estimates) MLE.

The “gevfit” function returns MLE of the parameters for the generalized extreme value (GEV) distribution. You can refer an example code below for better understanding:

% Generate some sample data 
data = evrnd(0, 1, 50, 1);  % Generating 50 random numbers from a Gumbel distribution with location 0 and scale 1 

% Fit a Gumbel distribution to the dataset 
[param, param_CIs] = gevfit(data); 

% Display the estimated parameters and their confidence intervals 
disp('Estimated Parameters:'); 

Estimated Parameters:

disp(param); 

   -0.4894    1.4690   -1.1317

disp('Confidence Intervals for Parameters:'); 

Confidence Intervals for Parameters:

disp(param_CIs); 

   -0.6697    1.1680   -1.5749
   -0.3090    1.8476   -0.6884

For more information on the “evrnd” and “gevfit” function, refer the links below:

• “evrnd” : https://www.mathworks.com/help/stats/evrnd.html
• “gevfit” : https://www.mathworks.com/help/stats/gevfit.html

Regards,

Ayush