MATLAB: Maximum likelihood did not converge for gevfit

extrem value distributionsgeneralized extreme value distributiongevfitMATLABmaximum likelihoodmaximum likelihood did not convergemlemle did not converge

I am trying to fit a generalized extreme value distribution usinf the functioin of "gevfit" as well as the "fitdist" to a rainfall data set which is as follows
1028.5
860.3
1088.2
711.6
874.3
776.2
973.7
457.9 
pdGEV=fitdist(sample,'Generalizedextremevalue'); % probability  distribution object
paraGEV= gevfit(sample); % paramter estimation
Parameters are calculated are as follows 
'shape'  k  =  -1.03801443465120	'scale'  sigma   =  273.595539473463 	'location'  mu   =  824.624147545310 		
but there is a warning message
Warning: Maximum likelihood estimation did not converge.  Function evaluation limit exceeded. 
> In gevfit (line 115)
  In prob.GeneralizedExtremeValueDistribution.fit (line 170)
  In fitdist>localfit (line 238)
  In fitdist (line 185)
  In newcode (line 271) 
Warning: Maximum likelihood has converged to a boundary point of the parameter space.
Confidence intervals and standard errors cannot be computed reliably. 
> In gevfit (line 127)
  In prob.GeneralizedExtremeValueDistribution.fit (line 170)
  In fitdist>localfit (line 238)
  In fitdist (line 185)
  In newcode (line 271) 
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND =  7.552473e-21. 
> In gevlike (line 94)
  In prob.GeneralizedExtremeValueDistribution.fit (line 171)
  In fitdist>localfit (line 238)
  In fitdist (line 185)
  In newcode (line 271) 
Warning: Maximum likelihood estimation did not converge.  Function evaluation limit exceeded. 
> In gevfit (line 115)
  In newcode (line 272) 
Warning: Maximum likelihood has converged to a boundary point of the parameter space.
Confidence intervals and standard errors cannot be computed reliably. 
> In gevfit (line 127)
  In newcode (line 272)
How do I solve this problem?

Best Answer

I don't know for sure, but my best guess is that the problem is the relatively small amount of data, coupled with the fact that the GEV is difficult to fit because it has so much flexibility. (And the data don't really fit the shape, I think, but that is difficult to say with so little data.)
Can you use just the (non-generalized) extreme value distribution, or the Weibull distribution, for your application? Those both converge, presumably to sensible answers.
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