def testBijector(self):
with self.test_session():
scale = 5.
concentration = 0.3
bijector = tfb.Weibull(scale=scale,
concentration=concentration,
validate_args=True)
self.assertEqual("weibull", bijector.name)
x = np.array([[[0.], [1.], [14.], [20.], [100.]]],
dtype=np.float32)
# Weibull distribution
weibull_dist = stats.frechet_r(c=concentration, scale=scale)
y = weibull_dist.cdf(x).astype(np.float32)
self.assertAllClose(y, self.evaluate(bijector.forward(x)))
self.assertAllClose(x, self.evaluate(bijector.inverse(y)))
self.assertAllClose(
weibull_dist.logpdf(x),
self.evaluate(
bijector.forward_log_det_jacobian(x, event_ndims=0)))
self.assertAllClose(self.evaluate(
-bijector.inverse_log_det_jacobian(y, event_ndims=0)),
self.evaluate(
bijector.forward_log_det_jacobian(
x, event_ndims=0)),
rtol=1e-4,
atol=0.)
def testBijector(self):
with self.test_session():
scale = 5.
concentration = 0.3
bijector = Weibull(scale=scale,
concentration=concentration,
event_ndims=1,
validate_args=True)
self.assertEqual("weibull", bijector.name)
x = np.array([[[0.], [1.], [14.], [20.], [100.]]],
dtype=np.float32)
# Weibull distribution
weibull_dist = stats.frechet_r(c=concentration, scale=scale)
y = weibull_dist.cdf(x).astype(np.float32)
self.assertAllClose(y, bijector.forward(x).eval())
self.assertAllClose(x, bijector.inverse(y).eval())
self.assertAllClose(
# We should lose a dimension from calculating the determinant of the
# jacobian.
np.squeeze(weibull_dist.logpdf(x), axis=2),
bijector.forward_log_det_jacobian(x).eval())
self.assertAllClose(-bijector.inverse_log_det_jacobian(y).eval(),
bijector.forward_log_det_jacobian(x).eval(),
rtol=1e-4,
atol=0.)
def testBijector(self):
scale = 5.
concentration = 0.3
bijector = tfb.Weibull(
scale=scale, concentration=concentration, validate_args=True)
self.assertEqual("weibull", bijector.name)
x = np.array([[[0.], [1.], [14.], [20.], [100.]]], dtype=np.float32)
# Weibull distribution
weibull_dist = stats.frechet_r(c=concentration, scale=scale)
y = weibull_dist.cdf(x).astype(np.float32)
self.assertAllClose(y, self.evaluate(bijector.forward(x)))
self.assertAllClose(x, self.evaluate(bijector.inverse(y)))
self.assertAllClose(
weibull_dist.logpdf(x),
self.evaluate(bijector.forward_log_det_jacobian(x, event_ndims=0)))
self.assertAllClose(
self.evaluate(-bijector.inverse_log_det_jacobian(y, event_ndims=0)),
self.evaluate(bijector.forward_log_det_jacobian(x, event_ndims=0)),
rtol=1e-4,
atol=0.)
def testBijector(self):
with self.test_session():
scale = 5.
concentration = 0.3
bijector = Weibull(
scale=scale, concentration=concentration,
event_ndims=1, validate_args=True)
self.assertEqual("weibull", bijector.name)
x = np.array([[[0.], [1.], [14.], [20.], [100.]]], dtype=np.float32)
# Weibull distribution
weibull_dist = stats.frechet_r(c=concentration, scale=scale)
y = weibull_dist.cdf(x).astype(np.float32)
self.assertAllClose(y, bijector.forward(x).eval())
self.assertAllClose(x, bijector.inverse(y).eval())
self.assertAllClose(
# We should lose a dimension from calculating the determinant of the
# jacobian.
np.squeeze(weibull_dist.logpdf(x), axis=2),
bijector.forward_log_det_jacobian(x).eval())
self.assertAllClose(
-bijector.inverse_log_det_jacobian(y).eval(),
bijector.forward_log_det_jacobian(x).eval(),
rtol=1e-4,
atol=0.)
mean, var, skew, kurt = frechet_r.stats(c, moments='mvsk')
# Display the probability density function (``pdf``):
x = np.linspace(frechet_r.ppf(0.01, c),
frechet_r.ppf(0.99, c), 100)
ax.plot(x, frechet_r.pdf(x, c),
'r-', lw=5, alpha=0.6, label='frechet_r 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 = frechet_r(c)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# Check accuracy of ``cdf`` and ``ppf``:
vals = frechet_r.ppf([0.001, 0.5, 0.999], c)
np.allclose([0.001, 0.5, 0.999], frechet_r.cdf(vals, c))
# True
# Generate random numbers:
r = frechet_r.rvs(c, size=1000)
# And compare the histogram:
ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
def test_Exponential_to_Weibull(self):
X = RV(Exponential(rate=5))
sims = X.sim(Nsim)
cdf = stats.frechet_r(scale=1 / 5, c=1).cdf
pval = stats.kstest(sims, cdf).pvalue
self.assertTrue(pval > .01)
from scipy.stats import frechet_r import matplotlib.pyplot as plt import numpy as np fig, ax = plt.subplots(1, 1) F = frechet_r(loc=17.440, scale=8.153, c=0.198) x = np.arange(0.01, 120, 0.01) ax.plot(x, F.pdf(x), 'k-', lw=2) plt.show()