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fit-hyperbolic.py

import numpy as np
from scipy.stats import norm
from sklearn.mixture import GaussianMixture
from scipy.stats import genhyperbolic
import json
import matplotlib.pyplot as plt

with open('./data.json', 'r') as file:
  sample = json.load(file)

# Build empirical CDF
sorted_sample = np.sort(sample)
cdf_e = np.arange(1, len(sorted_sample) + 1) / len(sorted_sample)
ccdf_e = 1 - cdf_e

# Fit Hyperbolic
p, a, b, loc, scale = genhyperbolic.fit(np.array(sample), floc=0, fscale=1)

# Compute CCDF from fitted hyperbolic
ccdf_h = 1 - genhyperbolic.cdf(sorted_sample, p, a, b, loc=loc, scale=scale)

# Plot linearly
plt.figure()
plt.plot(sorted_sample, ccdf_e, label="Empirical CCDF", linestyle='--')
plt.plot(sorted_sample, ccdf_h, label="Fitted Hyperbolic CCDF", linestyle='-')
plt.xlim(0.01, 0.5)
plt.ylim(0, 0.5)
plt.xlabel('x')
plt.ylabel('CCDF')
plt.title('CCDF (Linear Scale)')
plt.grid(True)
plt.legend()
plt.show()

# Plot log-log
plt.figure()
plt.loglog(sorted_sample, ccdf_e, label="Empirical CCDF", linestyle='--')
plt.loglog(sorted_sample, ccdf_h, label="Fitted Hyperbolic CCDF", linestyle='-')
plt.xlim(0.1, 1)
plt.ylim(0.001, 0.5)
plt.xlabel('x (log scale)')
plt.ylabel('CCDF (log scale)')
plt.title('CCDF (Log-Log Scale)')
plt.grid(True, which="both", ls="--")
plt.legend()
plt.show()