tailestim 0.1.1

A Python package for estimating tail parameters of heavy-tailed distributions, which is useful for analyzing power-law behavior in complex networks.

tailestim

A Python package for estimating tail parameters of heavy-tailed distributions, which is useful for analyzing power-law behavior in complex networks.

[!NOTE] The original estimation implementations are from ivanvoitalov/tail-estimation, which is based on the paper (Voitalov et al. 2019). tailestim is a wrapper package that provides a more convenient/modern interface and logging, that can be installed using pip and conda.

Features

• Multiple estimation methods including Hill, Moments, Kernel, Pickands, and Smooth Hill estimators
• Double-bootstrap procedure for optimal threshold selection
• Built-in example datasets

Installation

pip install tailestim

Quick Start

Using Built-in Datasets

from tailestim import TailData
from tailestim import HillEstimator, KernelTypeEstimator, MomentsEstimator

# Load a sample dataset
data = TailData(name='CAIDA_KONECT').data

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

# Get the estimated parameters
result = estimator.get_parameters()
gamma = result['gamma']

# Print full results
print(estimator)

Using degree sequence from networkx graphs

import networkx as nx
from tailestim import HillEstimator, KernelTypeEstimator, MomentsEstimator

# Create or load your network
G = nx.barabasi_albert_graph(10000, 2)
degree = list(dict(G.degree()).values()) # Degree sequence

# Initialize and fit the Hill estimator
estimator = HillEstimator()
estimator.fit(degree)

# Get the estimated parameters
result = estimator.get_parameters()
gamma = result['gamma']

# Print full results
print(estimator)

Available Estimators

The package provides several estimators for tail estimation. For details on parameters that can be specified to each estimator, please refer to the original repository ivanvoitalov/tail-estimation, original paper, or the actual code.

1. Hill Estimator (HillEstimator)
   • Classical Hill estimator with double-bootstrap for optimal threshold selection
   • Generally recommended for power law analysis
2. Moments Estimator (MomentsEstimator)
   • Moments-based estimation with double-bootstrap
   • More robust to certain types of deviations from pure power law
3. Kernel-type Estimator (KernelEstimator)
   • Kernel-based estimation with double-bootstrap and bandwidth selection
4. Pickands Estimator (PickandsEstimator)
   • Pickands-based estimation (no bootstrap)
   • Provides arrays of estimates across different thresholds
5. Smooth Hill Estimator (SmoothHillEstimator)
   • Smoothed version of the Hill estimator (no bootstrap)

Results

The full result can be obtained by estimator.get_parameters(), which returns a dictionary. This includes:

• gamma: Power law exponent (γ = 1 + 1/ξ)
• xi_star: Tail index (ξ)
• k_star: Optimal order statistic
• Bootstrap results (when applicable):
  • First and second bootstrap AMSE values
  • Optimal bandwidths or minimum AMSE fractions

Example Output

When you print(estimator) after fitting, you will get the following output.

==================================================
Tail Estimation Results (HillEstimator)
==================================================

Parameters:
--------------------
Optimal order statistic (k*): 26708
Tail index (ξ): 0.3974
Gamma (powerlaw exponent) (γ): 3.5167

Bootstrap Results:
--------------------
First bootstrap minimum AMSE fraction: 0.2744
Second bootstrap minimum AMSE fraction: 0.2745

Built-in Datasets

The package includes several example datasets:

• CAIDA_KONECT
• Libimseti_in_KONECT
• Pareto

Load any example dataset using:

from tailestim import TailData
data = TailData(name='dataset_name').data

Loaded data

References

• I. Voitalov, P. van der Hoorn, R. van der Hofstad, and D. Krioukov. Scale-free networks well done. Phys. Rev. Res., Oct. 2019, doi: 10.1103/PhysRevResearch.1.033034.
• I. Voitalov. ivanvoitalov/tail-estimation, GitHub. Mar. 2018. https://github.com/ivanvoitalov/tail-estimation.

License

tailestim is distributed under the terms of the MIT license.