estimators.moment

class evt.estimators.moment.Moment(peaks_over_threshold: evt.methods.peaks_over_threshold.PeaksOverThreshold)

Bases: evt.estimators.estimator_abc.Estimator

Moment estimator for the tail index in the peaks over threshold approach. [1] Also known as the Dekkers-Einmahl-De Haan estimator. [2]

The number of order statistics number_of_order_statistics to use in the estimate must be specified. Contains a plotting routine for the moment estimator against the number of order statistics. Confidence intervals are based on the asymptotic behaviour of the variance of the estimate. Bias is not taken into account.

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

  2. Dekkers, Arnold LM, John HJ Einmahl, and Laurens De Haan. “A moment estimator for the index of an extreme-value distribution.” The Annals of Statistics (1989): 1833-1855.

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

Returns the moment estimate for the tail index \gamma \in \mathbb{R}, calculated with number_of_order_statistics order statistics. [1]

Confidence intervals are based on the asymptotic behaviour of the variance of the estimate. [1] Bias is not taken into account.

Parameters

number_of_order_statistics – number of order statistics to use in the moment estimator. Must be bigger than zero and smaller than the number of peaks in the peaks over threshold approach.

Returns

Estimate of the tail index.

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

plot(ax: matplotlib.axes._axes.Axes, max_number_of_order_statistics: Optional[int] = None)

Plots the moment estimate against the number of order statistics.

The maximum number of order statistics to use in the plot can be specified by max_number_of_order_statistics. If None, the maximum number of order statistics will be the number of peaks in the peaks over threshold approach, minus one.