def plot_wikipedia_pmfs():
"""
https://en.wikipedia.org/wiki/Binomial_distribution#/media/File:Binomial_distribution_pmf.svg
"""
ax = new_axes()
Binomial(n=20, p=0.5).plot(k=k_wiki,
kind='line',
color='blue',
ax=ax,
ls='',
marker='d')
Binomial(n=20, p=0.7).plot(k=k_wiki,
kind='line',
color='lightgreen',
ax=ax,
ls='',
marker='s')
Binomial(n=40, p=0.5).plot(k=k_wiki,
kind='line',
color='red',
ax=ax,
ls='',
marker='o')
ax.set_ylim(0, 0.25)
ax.set_title('Probability mass function')
ax.legend(loc='upper right')
plt.show()
def plot_scipy_pmf():
"""
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.binom.html
"""
ax = Binomial(n=5, p=0.4).plot(
k=range(0, 5), kind='line', ls='', marker='o', color='blue', vlines=True
)
ax.set_xlim(-0.5, 4.5)
plt.show()
def plot_ml_app_pmfs():
"""
Machine Learning: A Probabilistic Perspective. Figure 2.4
"""
_, ax = plt.subplots(ncols=2, figsize=(16, 9))
Binomial(n=10, p=0.25).plot(k=k_ml_app, color=ML_APP_DARK_BLUE, ax=ax[0])
ax[0].legend(loc='upper right')
Binomial(n=10, p=0.9).plot(k=k_ml_app, color=ML_APP_DARK_BLUE, ax=ax[1])
ax[1].legend(loc='upper left')
plt.show()
def plot_wikipedia_cdfs():
"""
https://en.wikipedia.org/wiki/Binomial_distribution#/media/File:Binomial_distribution_cdf.svg
"""
ax = new_axes()
Binomial(n=20, p=0.5).cdf().plot(k=k_wiki,
kind='line',
color='blue',
ax=ax)
Binomial(n=20, p=0.7).cdf().plot(k=k_wiki,
kind='line',
color='lightgreen',
ax=ax)
Binomial(n=40, p=0.5).cdf().plot(k=k_wiki, kind='line', color='red', ax=ax)
ax.set_ylim(0, 1.0)
ax.set_title('Cumulative distribution function')
ax.legend(loc='upper right')
plt.show()
def likelihood(self) -> Binomial:
"""
Return a distribution reflecting the likelihood of observing
the data, under a Binomial model, independent of the prior belief about
the distribution of parameter p.
"""
return Binomial(
n=self._n,
p=self._k / self._n
)
def likelihood(self, m: Optional[int] = None) -> Binomial:
m = m if m is not None else self._m
return Binomial(n=self._n,
p=m / self._n).with_x_label('k') # * comb(n, k)
def __getitem__(self, item) -> Binomial:
return Binomial(
n=self._n, p=self._p[item]
)