estimators.gevmle

class evt.estimators.gevmle.GEVMLE(block_maxima: evt.methods.block_maxima.BlockMaxima)

Bases: evt.estimators.estimator_abc.Estimator

Maximum likelihood estimator for the generalized extreme value distribution in the block maxima approach with distribution

\exp \bigg[ -(1+ \gamma (x - \mu) / \sigma) ^{-1/\gamma} \bigg]

where

  • self.tail_index corresponds to the tail index \gamma,

  • self.loc corresponds to the location parameter \mu,

  • self.scale corresponds to the scale parameter \sigma.

Confidence intervals are estimated using the observed Fisher information.

estimate() → List[evt.estimators.estimator_abc.Estimate]

Returns maximum likelihood estimates including confidence intervals for the tail index, location parameter and scale of the generalized extreme value distribution.

Estimates for the confidence intervals are based on asymptotic behaviour of the observed Fisher information for the generalized extreme value distribution.

The returned estimate might be only locally optimal or fail altogether. Moreover, if the confidence intervals are unable to be determined numerically, the .ci_lower and .ci_upper of the estimate will be nan.

Returns

maximum likelihood Estimate including confidence intervals for the tail index, location parameter and scale of the generalized extreme value distribution.

plot_qq_gev(ax: matplotlib.axes._axes.Axes)

Quantile-quantile plot of the empirical survival function of the block maxima against the fitted generalized extreme value distribution. The .estimate method must be called before this function.