def plot_wikipedia_pdfs_vs_normal():
"""
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/
File:T_distribution_1df_enhanced.svg
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/
File:T_distribution_2df_enhanced.svg
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/
File:T_distribution_3df_enhanced.svg
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/
File:T_distribution_5df_enhanced.svg
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/
File:T_distribution_10df_enhanced.svg
https://en.wikipedia.org/wiki/Student%27s_t-distribution#/media/
File:T_distribution_30df_enhanced.svg
"""
_, axes = plt.subplots(nrows=2, ncols=3, figsize=(16, 9))
normal = Normal(mu=0, sigma=1)
max_degrees = (1, 2, 3, 5, 10, 30)
for d in range(len(max_degrees)):
ax = axes.flat[d]
normal.plot(x=x_wikipedia_2, color='blue', ax=ax)
for d2 in range(d):
StudentsT(nu=max_degrees[d2]).plot(x=x_wikipedia_2, color='green',
alpha=0.5 ** (d - d2), ax=ax)
StudentsT(nu=max_degrees[d]).plot(x=x_wikipedia_2, color='red', ax=ax)
ax.legend(loc='upper right')
plt.show()
def test_fit(self):
for mu, sigma_sq in zip((0, 0, 0, -2), (0.2, 1.0, 5.0, 0.5)):
normal_orig = Normal(mu=mu, sigma_sq=sigma_sq)
normal_fit = Normal.fit(normal_orig.rvs(100_000))
self.assertAlmostEqual(normal_orig.mu, normal_fit.mu, 1)
self.assertAlmostEqual(normal_orig.sigma_sq, normal_fit.sigma_sq,
1)
def from_ratio_frame(data: DataFrame, name: str = ''):
"""
Create a new NormalSeries using the distributions of data in each
column of a DataFrame.
:param data: Data with ratio values.
:param name: Name for the Series.
"""
normals = {}
for col in data.columns:
normals[col] = Normal(mu=data[col].mean(), sigma=data[col].std())
normals = Series(data=normals, name=name)
return NormalSeries(normals)
def probably_greater_than(self, other: 'Ordinal') -> float:
"""
Find the approximate probability that self > other, assuming an
underlying Normal data generating distribution..
"""
m_self = self._data_vals.mean()
s_self = self._data_vals.std()
m_other = other._data_vals.mean()
s_other = other._data_vals.std()
m_diff = m_self - m_other
s_diff = (s_self ** 2 + s_other ** 2) ** 0.5
diff = Normal(mu=m_diff, sigma=s_diff)
return diff > 0
def plot_normal_students_t_laplace():
"""
Machine Learning: A Probabilistic Perspective. Figure 2.7
"""
_, axes = plt.subplots(ncols=2, figsize=(16, 9))
# define distributions
normal = Normal(mu=0, sigma=1)
students_t = StudentsT(nu=1)
laplace = Laplace(mu=0, b=1 / sqrt(2))
# plot pdfs
ax = axes[0]
normal.plot(x=x, ls=':', color='black', ax=ax)
students_t.plot(x=x, ls='--', color=ML_APP_DARK_BLUE, ax=ax)
laplace.plot(x=x, ls='-', color='red', ax=ax)
ax.set_ylim(0, 0.8)
ax.legend(loc='upper right')
# plot log-pdfs
ax = axes[1]
normal.log_pdf().plot(x=x, ls=':', color='black', ax=ax)
students_t.log_pdf().plot(x=x, ls='--', color=ML_APP_DARK_BLUE, ax=ax)
laplace.log_pdf().plot(x=x, ls='-', color='red', ax=ax)
ax.set_ylim(-9, 0)
ax.legend(loc='upper right')
plt.show()
def setUp(self) -> None:
self.n1 = Normal(0, 1)
self.n2 = Normal(1, 2)