I would need to calculate the parameters of a 2-parameter Fréchet distribution with MS Excel for hundreds of samples. Could anyone point me to a source where I can find how to estimate the parameters of this distribution? I am aware that there is method through Least squares and Maximum Likelihood Estimators, but can't find a paper where any of them is clearly explained.
Also, any explanations on estimating the 3-parameters Fréchet would be more than welcome.
Thank you in advance.
since you have data you can try use the maximization methods available with softwares like R mathematuic to find MLE
Since you have a data set at hand, using packages like EasyFit or R will definitely give you the maximum likelihood estimates.
you can have an Excel-lent estimation through the "Solver" in Excel, which is a very good implementtion of a minimisation algorithm.
Hints :
1 - select two cells for introducing values of your requested parameters, put in there any values (will work with almost everything, but a sensible choice is enventually better)
2 - compute the log likelihood for each of your sample refering to these two cells
3 - sum them up and change the sign (because the algorithme seaks a min and you are looking for a max)
4 - refer to Excel for using the Solver on the 3 cells containig your parameters and the so-called "objective function" (i.e. minus the sum of the likelihoods)
caveats :
"Solver" may not be activated in the standard setting of Excel, have a look at the "Help" to see how to activate it
you won't get any indication of the precision of your estimates - for that you must revert to a stat software (R amonst others) but tests are available through the log-likelihood ratio tests.
Thanks to all of you, BUT I can't do it with optimization methods. I need to develop a spreadsheet that calculates approximately 500 fits to a 500 different Fréchet distributions each time. So Solver, Esay fit, etc are not an option. I need the mathematical expressions to calculate the Fréchet parameters indeed.
the general Frechet distribution has three parameters : shape, center and scale - what is the exact algebraic expression of yours ?
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