Hill Estimator#

class tailestim.estimators.hill.HillEstimator(bootstrap=True, t_bootstrap=0.5, r_bootstrap=500, eps_stop=0.99, verbose=False, diagn_plots=False, base_seed=None, max_resample=50, **kwargs)[source]#

Bases: BaseTailEstimator

Hill estimator for tail index estimation.

This class implements the Hill estimator with optional double-bootstrap for optimal threshold selection.

Parameters:

bootstrapbool, default=True: Whether to use double-bootstrap for optimal threshold selection.
t_bootstrapfloat, default=0.5: Parameter controlling the size of the 2nd bootstrap. Defined from n2 = n*(t_bootstrap).
r_bootstrapint, default=500: Number of bootstrap resamplings for the 1st and 2nd bootstraps.
eps_stopfloat, default=0.99: Parameter controlling range of AMSE minimization. Defined as the fraction of order statistics to consider during the AMSE minimization step.
verbosebool, default=False: Flag controlling bootstrap verbosity.
diagn_plotsbool, default=False: Flag to switch on/off generation of AMSE diagnostic plots.
base_seed: None | SeedSequence | BitGenerator | Generator | RandomState, default=None: Base random seed for reproducibility of bootstrap.
max_resampleint, default=50: Maximum number of resampling attempts when the double-bootstrap detects a false AMSE minimum (k2 > k1). Raises RuntimeError if exceeded.

__init__(bootstrap=True, t_bootstrap=0.5, r_bootstrap=500, eps_stop=0.99, verbose=False, diagn_plots=False, base_seed=None, max_resample=50, **kwargs)[source]#

get_params()[source]#

Get the parameters of the estimator.

Returns:

dict: Dictionary containing the parameters of the estimator.

get_result()[source]#

Get the estimated parameters.

Attributes:

estimatorBaseTailEstimator: The estimator instance (e.g., HillEstimator, PickandsEstimator, etc.) used for estimation.
xi_star_float: Optimal tail index estimate (ξ).
gamma_float: Power law exponent (γ).
k_arr_np.ndarray: Array of order statistics.
xi_arr_np.ndarray: Array of tail index estimates.
k_star_float: Optimal order statistic (k*).
bootstrap_results_dict: Bootstrap results.

Returns:

TailEstimatorResult

Examples#

from tailestim import TailData
from tailestim import HillEstimator

data = TailData(name='Pareto').data

# Initialize and fit Hill estimator
hill = HillEstimator()
hill.fit(data)

# Get estimated values
res = hill.get_result()

Hill Estimator#

Examples#

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