def cauchyFunc():
for i in range(len(size)):
n = size[i]
fig, ax = plt.subplots(1, 1)
ax.set_title("Распределение Коши, n = " + str(n))
x = np.linspace(cauchy.ppf(0.01), cauchy.ppf(0.99), 100)
ax.plot(x, cauchy.pdf(x), 'b-', lw=5, alpha=0.6)
r = cauchy.rvs(size=n)
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
plt.show()
def ppf(self, q):
"""
Percentile function (inverse cumulative distribution function)
:param q: np.ndarray, quantiles to evaluate
:return: np.ndarray, quantiles
"""
return cauchy.ppf(q, self.mu, self.eta)
def test_voigt_ppf():
resonance_energy = 1e6
pseudo_voigt = PseudoVoigtDistribution(resonance_energy, 1.0, 1.0, 100.0)
# Test scalar and array input.
assert np.isclose(pseudo_voigt.ppf(0.5), resonance_energy, 1e-5)
assert np.allclose(
pseudo_voigt.ppf(np.array([0.5, 0.5])),
np.array([resonance_energy, resonance_energy]),
1e-5,
)
# Test fallback approximation.
# The result should be somewhere in between the results of the two constituent PPFs.
extremely_small_quantile = 1e-7
with pytest.warns(UserWarning):
assert pseudo_voigt.ppf(extremely_small_quantile) > cauchy.ppf(
extremely_small_quantile
)
assert pseudo_voigt.ppf(extremely_small_quantile) < norm.ppf(
extremely_small_quantile
)
def tune_scale(self, u: float, y: float):
self.scale = abs(u - y) / cauchy.ppf(q=((self.p + 1) / 2))
#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import cauchy
fig, ax = plt.subplots(figsize=(8, 7))
ax.set_xlim([0.4, 0.68])
ax.set_ylim([0, 9.5])
mean, var, skew, kurt = cauchy.stats(moments='mvsk')
x = np.linspace(cauchy.ppf(0.01), cauchy.ppf(0.99), 1000000)
y = np.linspace(0, 6.6, 100)
ons = np.ones(100)
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
fsize = 18
#2c0032
ax.plot(x, cauchy.pdf(x, loc=0.53432, scale=0.0382), color='#6ca6cd',
lw=3) #, label='$\Delta=0.0382, \sigma=0.0079$')
#ax.plot(x, cauchy.pdf(x, loc=0.55334, scale=0.0102 ), color='#8c07ee', lw=3, label='$\Delta=0.0102$')
#ax.plot(x, cauchy.pdf(x, loc=0.54545, scale=0.0024 ), color='#ad1927', lw=3, label='$\Delta=0.0024$')
#ax.plot(x, cauchy.pdf(x, loc=0.59613, scale=0.0988 ), color='#f5ce00', lw=3, label='$\Delta=0.0988$')
#ax.plot(x, cauchy.pdf(x, loc=0.53622, scale=0.0349 ), color='#ff6600', lw=3, label='$\Delta=0.0349$')
midp = 0.5 * (0.488 + 0.580)
from scipy.stats import cauchy import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) # Calculate a few first moments: mean, var, skew, kurt = cauchy.stats(moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(cauchy.ppf(0.01), cauchy.ppf(0.99), 100) ax.plot(x, cauchy.pdf(x), 'r-', lw=5, alpha=0.6, label='cauchy 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 = cauchy() ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = cauchy.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], cauchy.cdf(vals)) # True # Generate random numbers: r = cauchy.rvs(size=1000)
#!/usr/bin/python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import cauchy
fig, ax = plt.subplots(1,1)
mean,var,skew,kurt = cauchy.stats(moments='mvsk')
x = np.linspace(cauchy.ppf(0.01),cauchy.ppf(0.99),100000)
y = np.linspace(0,140,100)
y2 = np.linspace(0,80,100)
ons = np.ones(100)
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
ax.plot(x, cauchy.pdf(x, loc=0.53432, scale=0.0382 ), color='#2c0032', lw=3, label='$\Delta=0.0382$')
ax.plot(x, cauchy.pdf(x, loc=0.55334, scale=0.0102 ), color='#8c07ee', lw=3, label='$\Delta=0.0102$')
ax.plot(x, cauchy.pdf(x, loc=0.54545, scale=0.0024 ), color='#ad1927', lw=3, label='$\Delta=0.0024$')
ax.plot(x, cauchy.pdf(x, loc=0.59613, scale=0.0988 ), color='#f5ce00', lw=3, label='$\Delta=0.0988$')
ax.plot(x, cauchy.pdf(x, loc=0.53622, scale=0.0349 ), color='#ff6600', lw=3, label='$\Delta=0.0349$')
ax.plot(x, cauchy.pdf(x, loc=0.5237, scale=0.0295 ), color='#6ca6cd', lw=3, label='$\Delta=0.0295$')
ax.plot(0.695*ons,y2,'k--',lw=1)
ax.plot(0.494*ons,y,'k--',lw=1)
ax.legend(loc='best',frameon=False)
ax.set_xlim([0.425,0.75])
#ax.set_title('Cauchy PDF')
#plt.text(-2.0,0.2,'$\Delta=0.53$',fontsize=12)
x3 = np.linspace(min(laplace.ppf(0.01), min(r3)),
max(laplace.ppf(0.99), max(r3)), 100)
ax[2].plot(x3, laplace.cdf(x3, 0, sqrt(2)))
ax[2].hist(r3,
density=True,
bins=floor(len(r3)),
histtype='step',
cumulative=True)
ax[2].set_xlabel('x')
ax[2].set_title('Распределение Лапласа, n=100')
#plt.show()#Лапласа
fig2, ay = plt.subplots(1, 3)
r = cauchy.rvs(size=20)
y = np.linspace(min(cauchy.ppf(0.01), min(r)), max(cauchy.ppf(0.99), max(r)),
100)
ay[0].plot(y, cauchy.cdf(y, 0, 1))
ay[0].hist(r,
density=True,
bins=floor(len(r)),
histtype='step',
cumulative=True)
ay[0].set_xlabel('x')
ay[0].set_title('Распределение Коши, n=20')
r2 = cauchy.rvs(size=60)
y2 = np.linspace(min(cauchy.ppf(0.01), min(r2)), max(cauchy.ppf(0.99),
max(r2)), 100)
ay[1].plot(y2, cauchy.cdf(y2, 0, 1))
ay[1].hist(r2,
def vot_distribution(sample_size, loc=10, scale=3):
x = np.linspace(cauchy.ppf(0.01), cauchy.ppf(0.99), 1000)
rv = cauchy(loc, scale)
y = rv.pdf(x)
samples = rv.rvs(size=size)
return samples