How to determine the parameters of statistical distributions

Hey, I have a dataset which consist of hourly wind speed points. I would like to know ho to use the "mle" command to determine the estimates for the parameters of a weibull, rayleigh, gamma and chi-square distribution?

Answer 1

[Star Strider]

Use the Statistics and Machine Learning Toolbox fitdist (link) function.

[vedesh Mohit]

I tried using the distribution fitter app in matlab, however when I import my data, the distributions that I am looking at do not appear in the drop down menu. All my data points are positive so I don't understand what is going on.

[vedesh Mohit]

I used the fitdist function [pd = fitdist(x,'Weibull')], but this error comes up

Error in fitdist (line 185) pd = localfit(dist,fitter,x,cens,freq,args{:});

Error in normaldisttt (line 14381) pd = fitdist(x,'Weibull')

[Star Strider]

Note that fitdist is a function, not an app. See if you can use it to fit your data. You should have access to it.

[vedesh Mohit]

Yea I know fitdist is not an app, I was just testing out the distribution fitter app because it has these distributions built in already. However I think the issue that I am facing is that even if I use the app or the fitdist function, my wind speed data consist of points with the value 0 and these distribution does not consider zero to be a positive integer. Is there a way I could go about doing this? If I exclude the zeros, would that be considering as biasing the results?

[Star Strider]

I usually substitute a very small scalar for zero entries, usually 1E-7, 1E-8 (essentially sqrt(eps)) or something in that range. I choose the magnitude so that squaring it remains a very small scalar, rather than zero, since zero could result in non-finite results. That also does not (in my experience at least) significantly affect the estimated distribution parameters.

However it could affect the parameter values if the rest of your data have very small amplitudes as well. The only solution for that might be to do your calculations in the Symbolic Math Toolbox, where extended precision is allowed. Then you could use an even smaller symbolic scalar to substitute for zero values.