estimators.gpdmle

class evt.estimators.gpdmle.GPDMLE(peaks_over_threshold: evt.methods.peaks_over_threshold.PeaksOverThreshold)

Bases: evt.estimators.estimator_abc.Estimator

Maximum likelihood estimator for the generalized Pareto distribution in the peaks over threshold approach with distribution

1 - (1+ \gamma (x - \mu) / \sigma) ^{-1/\gamma}

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.

The tail index \gamma and scale parameter \sigma can be estimated. The location parameter \mu is taken from the peaks over threshold method peaks_over_threshold.

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

Returns maximum likelihood estimates including confidence intervals for the tail index and scale of the generalized Pareto distribution.

The estimator behaves irregularly for \gamma \leq -\frac{1}{2}. [1] Confidence intervals are based on the asymptotic behaviour of the variance of the estimate. [1] Bias is not taken into account. The returned estimate might be only locally optimal or fail altogether.

Returns

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

  1. De Haan, Laurens, and Ana Ferreira. Extreme value theory: an introduction. Springer Science & Business Media, 2007.

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

Quantile-quantile plot of the empirical survival function of the peaks against the fitted generalized Pareto distribution. The .estimate method must be called before this function.