def xtalball(x, *p):
if len(p) == 5:
mu, sigma, A, beta, m = p
else:
print(
"Incorrect usage of crystal ball function! params: mu, sigma, area, beta, m. You input: {}"
.format(p))
exit(0)
return A * crystalball.pdf(x, beta, m, loc=mu, scale=sigma)
def xtalball(x, mu, sigma, A, beta, m):
"""
power-law tail plus gaussian https://en.wikipedia.org/wiki/Crystal_Ball_function
"""
return A * crystalball.pdf(x, beta, m, loc=mu, scale=sigma)
import numpy as np
from scipy.stats import moyal, crystalball
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# plot moyal pdf
loc, scale = 0, 0.625
x = np.linspace(moyal.ppf(0.01, loc, scale), moyal.ppf(0.99, loc, scale), 100)
ax.plot(x, moyal.pdf(x, loc, scale), 'r-', alpha=0.6, label='moyal pdf')
# plot crystal ball pdf
beta, m = 2, 3
x = np.linspace(crystalball.ppf(0.01, beta, m), crystalball.ppf(0.99, beta, m),
100)
ax.plot(x,
crystalball.pdf(x, beta, m),
'b-',
alpha=0.6,
label='crystalball pdf')
plt.legend()
plt.show()
def density_function(x):
return crystalball.pdf(x, beta=abs(alpha), m=n, loc=-mu, scale=sigma)
def density_function(x):
return crystalball.pdf(x, 1.11, 1.37, -85.6, 55.37)
def density_function(x):
return crystalball.pdf(x, 0.99, 1.6, -60.5, 16.3)
def test_cb_dcb():
obs = zfit.Space('x', limits=bounds)
mu_ = zfit.Parameter('mu_cb5', mu)
sigma_ = zfit.Parameter('sigma_cb5', sigma)
alphal_ = zfit.Parameter('alphal_cb5', alphal)
nl_ = zfit.Parameter('nl_cb5', nl)
alphar_ = zfit.Parameter('alphar_cb5', alphar)
nr_ = zfit.Parameter('nr_cb5', nr)
cbl = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=alphal_, n=nl_)
cbr = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=-alphar_, n=nr_)
dcb = DoubleCB(obs=obs,
mu=mu_,
sigma=sigma_,
alphal=alphal_,
nl=nl_,
alphar=alphar_,
nr=nr_)
sample_testing(cbl)
sample_testing(cbr)
sample_testing(dcb)
x = np.random.normal(mu, sigma, size=10000)
probsl = eval_testing(cbl, x)
probsr = eval_testing(cbr, x)
assert not any(np.isnan(probsl))
assert not any(np.isnan(probsr))
probsl_scipy = crystalball.pdf(x, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-x, beta=alphar, m=nr, loc=mu, scale=sigma)
ratio_l = probsl_scipy / probsl
ratio_r = probsr_scipy / probsr
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
kwargs = dict(limits=(-5.0, mu), norm_range=lbounds)
intl = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy()) == 0.
intl = cbr.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy()) != 0
kwargs = dict(limits=(mu, 2.0), norm_range=rbounds)
intr = cbr.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intr.numpy()) == 0.
intr = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intr.numpy()) != 0.
xl = x[x <= mu]
xr = x[x > mu]
probs_dcb_l = eval_testing(dcb, xl)
probs_dcb_r = eval_testing(dcb, xr)
probsl_scipy = crystalball.pdf(xl, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-xr, beta=alphar, m=nr, loc=mu, scale=sigma)
ratio_l = probsl_scipy / probs_dcb_l
ratio_r = probsr_scipy / probs_dcb_r
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
def test_cb_dcb():
obs = zfit.Space("x", limits=bounds)
mu_ = zfit.Parameter("mu_cb5", mu)
sigma_ = zfit.Parameter("sigma_cb5", sigma)
alphal_ = zfit.Parameter("alphal_cb5", alphal)
nl_ = zfit.Parameter("nl_cb5", nl)
alphar_ = zfit.Parameter("alphar_cb5", alphar)
nr_ = zfit.Parameter("nr_cb5", nr)
cbl = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=alphal_, n=nl_)
cbr = CrystalBall(obs=obs, mu=mu_, sigma=sigma_, alpha=-alphar_, n=nr_)
dcb = DoubleCB(obs=obs,
mu=mu_,
sigma=sigma_,
alphal=alphal_,
nl=nl_,
alphar=alphar_,
nr=nr_)
sample_testing(cbl)
sample_testing(cbr)
sample_testing(dcb)
x = np.random.normal(mu, sigma, size=10000)
probsl = eval_testing(cbl, x)
probsr = eval_testing(cbr, x)
assert not any(np.isnan(probsl))
assert not any(np.isnan(probsr))
probsl_scipy = crystalball.pdf(x, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-x + 2 * mu,
beta=alphar,
m=nr,
loc=mu,
scale=sigma)
# We take the ration as the normalization is not fixed
ratio_l = probsl_scipy / probsl
ratio_r = probsr_scipy / probsr
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
kwargs = dict(limits=(-5.0, mu), norm_range=lbounds)
intl = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy(), abs=1e-3) == 0.0
intl = cbr.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intl.numpy(), abs=1e-3) != 0
# TODO: update test to fixed DCB integral
kwargs = dict(limits=(mu, 2.0), norm_range=rbounds)
dcb_integr1 = dcb.integrate(**kwargs)
intr = cbr.integrate(**kwargs) - dcb_integr1
assert pytest.approx(intr.numpy(), abs=1e-3) == 0.0
intr = cbl.integrate(**kwargs) - dcb.integrate(**kwargs)
assert pytest.approx(intr.numpy(), abs=1e-3) != 0.0
xl = x[x <= mu]
xr = x[x > mu]
probs_dcb_l = eval_testing(dcb, xl)
probs_dcb_r = eval_testing(dcb, xr)
probsl_scipy = crystalball.pdf(xl, beta=alphal, m=nl, loc=mu, scale=sigma)
probsr_scipy = crystalball.pdf(-xr + 2 * mu,
beta=alphar,
m=nr,
loc=mu,
scale=sigma)
ratio_l = probsl_scipy / probs_dcb_l
ratio_r = probsr_scipy / probs_dcb_r
assert np.allclose(ratio_l, ratio_l[0])
assert np.allclose(ratio_r, ratio_r[0])
rnd_limits = sorted(np.random.uniform(*bounds, 130))
integrals = []
for low, up in zip(rnd_limits[:-1], rnd_limits[1:]):
integrals.append(dcb.integrate((low, up), norm=False))
integral = np.sum(integrals)
integral_full = zfit.run(dcb.integrate((bounds[0], up), norm=False))
assert pytest.approx(integral_full, integral)
from scipy.stats import crystalball
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
beta, m = 2, 3
mean, var, skew, kurt = crystalball.stats(beta, m, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(crystalball.ppf(0.01, beta, m),
crystalball.ppf(0.99, beta, m), 100)
ax.plot(x, crystalball.pdf(x, beta, m),
'r-', lw=5, alpha=0.6, label='crystalball pdf')
# Alternatively, the distribution object can be called (as a function)
# to fix the shape, location and scale parameters. This returns a "frozen"
# RV object holding the given parameters fixed.
# Freeze the distribution and display the frozen ``pdf``:
rv = crystalball(beta, m)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = crystalball.ppf([0.001, 0.5, 0.999], beta, m)
np.allclose([0.001, 0.5, 0.999], crystalball.cdf(vals, beta, m))
# True