def plot_gamma_poisson_fit(data,
fit_results,
title=None,
x_label=None,
x_range=None,
y_range=None,
fig_size=(6, 5),
bin_width=1,
filename=None):
"""
:param data: (numpy.array) observations
:param fit_results: dictionary with keys "a", "gamma_scale", "loc"
:param title: title of the figure
:param x_label: label to show on the x-axis of the histogram
:param x_range: (tuple) x range
:param y_range: (tuple) y range
(the histogram shows the probability density so the upper value of y_range should be 1).
:param fig_size: int, specify the figure size
:param bin_width: bin width
:param filename: filename to save the figure as
"""
plot_fit_discrete(data=data,
dist=RVGs.GammaPoisson(
a=fit_results['a'],
gamma_scale=fit_results['gamma_scale'],
loc=fit_results['loc']),
label='Gamma-Poisson',
bin_width=bin_width,
title=title,
x_label=x_label,
x_range=x_range,
y_range=y_range,
fig_size=fig_size,
filename=filename)
def test_gamma_poisson(rnd, a, gamma_scale, loc=0):
# gamma-poisson random variate generator
gamma_poisson_dist = RVGs.GammaPoisson(a=a,
gamma_scale=gamma_scale,
loc=loc)
# obtain samples
samples = get_samples(gamma_poisson_dist, rnd)
# report mean and variance
print_test_results('GammaPoisson',
samples,
expectation=(a * gamma_scale) + loc,
variance=a * gamma_scale + a * (gamma_scale**2))
def test_fitting_gamma_poisson():
print("\nTesting Gamma Poisson with a=2, gamma_scale=4, loc=2")
dist = RVGs.GammaPoisson(a=2, gamma_scale=4, loc=2)
print(' percentile interval: ', dist.get_percentile_interval(alpha=0.05))
data = np.array(get_samples(dist, np.random))
dict_mm_results = RVGs.GammaPoisson.fit_mm(mean=np.average(data),
st_dev=np.std(data),
fixed_location=2)
dict_ml_results = RVGs.GammaPoisson.fit_ml(data=data, fixed_location=2)
print(" Fit:")
print(" MM:", dict_mm_results)
print(" ML:", dict_ml_results)
# plot the fitted distributions
Plot.plot_gamma_poisson_fit(data=data,
fit_results=dict_mm_results,
title='Method of Moment')
Plot.plot_gamma_poisson_fit(data=data,
fit_results=dict_ml_results,
title='Maximum Likelihood')
import numpy as np
import SimPy.RandomVariateGenerators as RVGs
# a random number generator
rng = np.random.RandomState(seed=0)
# gamma
gamma = RVGs.Gamma(a=0.9835458832943496, loc=0, scale=1.9199027077975956)
# generate 10 realizations from gamma
print('Realizations from gamma:')
for i in range(10):
print(gamma.sample(rng))
# gamma-Poisson
gammaPoisson = RVGs.GammaPoisson(a=0.3693765965041004,
gamma_scale=9.154827879319111,
loc=0)
# generate 10 realizations from gamma-Poisson
print('Realizations from gamma-Poisson:')
for i in range(10):
print(gammaPoisson.sample(rng))