estimators.hill

class evt.estimators.hill.Hill(peaks_over_threshold: evt.methods.peaks_over_threshold.PeaksOverThreshold)

Bases: evt.estimators.estimator_abc.Estimator

Hill estimator for the tail index in the peaks over threshold approach. [1]

The number of order statistics number_of_order_statistics to use in the estimate must be specified. Contains a plotting routine for the Hill estimator against the number of order statistics. Confidence intervals are based on the asymptotic behaviour of the variance of the estimate. [2] Bias is not taken into account.

1. Hill, Bruce M. “A simple general approach to inference about the tail of a distribution.” The annals of statistics (1975): 1163-1174.

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

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

Returns the Hill estimate for the tail index , calculated with number_of_order_statistics order statistics. [1]

Confidence intervals are based on the asymptotic behaviour of the variance of the estimate. [2] Bias is not taken into account.

Parameters

number_of_order_statistics – number of order statistics to use in the Hill 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. Hill, Bruce M. “A simple general approach to inference about the tail of a distribution.” The annals of statistics (1975): 1163-1174.

2. 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 Hill 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.