def gen_plot_bernoulli():
# generate bernoulli
print("\nBernoulli pmf w/ scipy.stats.bernoulli.pmf(0, p=0.3): {:.3f}".
format(bernoulli.pmf(0, p=0.3)))
print("\nBernoulli pmf w/ scipy.stats.bernoulli.pmf(range(3), p=0.3): {}".
format(bernoulli.pmf(range(3), p=0.3)))
print(
"\nBernoulli cdf w/ scipy.stats.bernoulli.cdf([0, 0.5, 1, 1.5], p=0.3): {}"
.format(bernoulli.cdf([0, 0.5, 1, 1.5], p=0.3)))
# plot Bernoulli
plt.stem([-0.2, 0, 1, 1.2], bernoulli.pmf([-0.2, 0, 1, 1.2], p=.3))
plt.plot(np.linspace(-0.1, 1.1, 1200),
bernoulli.cdf(np.linspace(-0.1, 1.1, 1200), p=0.3), 'g')
plt.xlim([-0.1, 1.1])
plt.ylim([-0.2, 1.1])
plt.show()
# generate Bernoulli samples
print(
"\nBernoulli samples w/ scipy.stats.bernoulli.rvs(size=10, p=.3): {}".
format(bernoulli.rvs(size=10, p=.3)))
plt.hist(bernoulli.rvs(size=10, p=.3), density=True)
plt.show()
return None
def cdf(self, x: float):
"""Find the CDF for a certain x value.
Args:
x (float): The value for which the CDF is needed.
"""
return bernoulli.cdf(x, self.p)
def get_bernoulli(p, size):
rv = bernoulli(p)
x = np.arange(0, np.minimum(rv.dist.b, 3))
h = plt.vlines(x, 0, rv.pmf(x), lw=2)
prb = bernoulli.cdf(x, p)
h = plt.semilogy(np.abs(x - bernoulli.ppf(prb, p)) + 1e-20)
labels = bernoulli.rvs(p, size=size).tolist()
return labels
def cdf(self):
"""
Compute the cumulative distribution function.
Returns:
--------
cdf : float
"""
return bernoulli.cdf(self.__r, self.__p)
def cdf(self, y, f):
r"""
Cumulative density function of the likelihood.
Parameters
----------
y: ndarray
query quantiles, i.e.\ :math:`P(Y \leq y)`.
f: ndarray
latent function from the GLM prior (:math:`\mathbf{f} =
\boldsymbol\Phi \mathbf{w}`)
Returns
-------
cdf: ndarray
Cumulative density function evaluated at y.
"""
return bernoulli.cdf(y, expit(f))
def cdf(self, y, f):
r"""
Cumulative density function of the likelihood.
Parameters
----------
y: ndarray
query quantiles, i.e.\ :math:`P(Y \leq y)`.
f: ndarray
latent function from the GLM prior (:math:`\mathbf{f} =
\boldsymbol\Phi \mathbf{w}`)
Returns
-------
cdf: ndarray
Cumulative density function evaluated at y.
"""
return bernoulli.cdf(y, expit(f))
def test_bernoulli():
# Test we can at match a Bernoulli distribution from scipy
p = 0.5
dist = lk.Bernoulli()
x = np.array([0, 1])
p1 = bernoulli.logpmf(x, p)
p2 = dist.loglike(x, p)
np.allclose(p1, p2)
p1 = bernoulli.cdf(x, p)
p2 = dist.cdf(x, p)
np.allclose(p1, p2)
plt.ylabel("Probability")
sns.despine()
plot_simulation(result)
from scipy.stats import bernoulli
brv = bernoulli(p=0.3)
brv.rvs(size=20)
event_space=[0,1]
plt.figure(figsize=(12,8))
colors=sns.color_palette()
for i, p in enumerate([0.1, 0.2, 0.5, 0.7]):
ax = plt.subplot(1, 4, i+1)
plt.bar(event_space, bernoulli.pmf(event_space, p), label=p, color = colors[i], alpha = 0.5)
plt.plot(event_space, bernoulli.cdf(event_space, p), color = colors[i], alpha=0.5)
ax.xaxis.set_ticks(event_space)
plt.ylim((0,1))
plt.legend(loc=0)
if i == 0:
plt.ylabel("PDF at $k$")
plt.tight_layout()
CDF = lambda x: np.float(np.sum(result < x))/result.shape[0]
for votes in [200, 300, 320, 340, 360, 400, 500]:
print "Obama Win CDF at votes=", votes, " is ", CDF(votes)
votelist = np.arange(0,540, 5)
plt.plot(votelist, [CDF(v) for v in votelist], '.-')
from scipy.stats import bernoulli, poisson, uniform, expon, erlang, norm, triang # Bernoulli p = 0.5 x = 1 # Generate a probability using the PMF print(bernoulli.pmf(x, p)) # 0.5 # Generate a probability using the CDF print(bernoulli.cdf(x, p)) # 1.0 # Generate three Bernoulli random numbers print(bernoulli.rvs(p, size=3)) # [0 1 0] # Poisson lmda = 2 x = 5 print(poisson.pmf(x, lmda)) print(poisson.cdf(x, lmda)) print(poisson.rvs(lmda, size=3)) # Uniform a = 3 b = 10 x = 10 print(uniform.pdf(x, loc=a, scale=(b - a))) # = 1 / 7 print(uniform.cdf(x, loc=a, scale=(b - a))) # = 1.0 print(uniform.rvs(loc=3, scale=(b - a), size=3)) # Exponential mu = 2 x = 2 print(expon.pdf(x, scale=(1 / mu)))
from scipy.stats import bernoulli
import numpy as np
import matplotlib.pyplot as plt
p = 0.8
k1 = 0
k2 = 1
k = np.linspace(k1, k2, 100)
temp1 = bernoulli.cdf(k, p)
temp2 = bernoulli.pmf(k1, p)
temp3 = bernoulli.pmf(k2, p)
print(temp1)
print(temp2)
print(temp3)
plt.plot(k, temp1, 'o-', color='orange')
plt.plot(p, temp2, 'o-', color='crimson')
plt.plot(p, temp3, 'o-', color='crimson')
plt.xlabel('$x$')
plt.ylabel('$y$')
plt.grid()
plt.show()
brv.rvs(size=20)
# In[20]:
event_space = [0, 1]
plt.figure(figsize=(12, 8))
colors = sns.color_palette()
for i, p in enumerate([0.1, 0.2, 0.5, 0.7]):
ax = plt.subplot(1, 4, i + 1)
plt.bar(event_space,
bernoulli.pmf(event_space, p),
label=p,
color=colors[i],
alpha=0.5)
plt.plot(event_space,
bernoulli.cdf(event_space, p),
color=colors[i],
alpha=0.5)
ax.xaxis.set_ticks(event_space)
plt.ylim((0, 1))
plt.legend(loc=0)
if i == 0:
plt.ylabel("PDF at $k$")
plt.tight_layout()
# In[21]:
CDF = lambda x: np.float(np.sum(result < x)) / result.shape[0]
for votes in [200, 300, 320, 340, 360, 400, 500]:
import seaborn as sns
# ### Bernoulli Distribution
# In[2]:
#Bernoulli Distribution
from scipy.stats import bernoulli
p = 0.7
x = np.arange(bernoulli.ppf(0.01, p), bernoulli.ppf(
0.99, p)) #Percent Point Function (inverse of cdf — percentiles)
print("Mean : ", bernoulli.stats(p, moments='m'))
print("Variance : ", bernoulli.stats(p, moments='v'))
print("Prob. Mass Func. : ", bernoulli.pmf(x, p).item())
print("Cum. Density Func.: ", bernoulli.cdf(x, p).item())
fig = plt.figure(figsize=(20, 10))
plt.subplot(221)
plt.plot(x, bernoulli.pmf(x, p), 'ro', ms=8, label='PMF=(1-p)')
plt.plot(1 - x, 1 - bernoulli.pmf(x, p), 'go', ms=8, label='PMF=p')
plt.vlines(x, 0, bernoulli.pmf(x, p), colors='r', lw=5, alpha=0.5)
plt.vlines(1 - x, 0, 1 - bernoulli.pmf(x, p), colors='g', lw=5, alpha=0.5)
plt.xlabel("Sample Space of Bernoulli Distribution", fontsize=14)
plt.ylabel("PMF", fontsize=14)
plt.title("Probability Distribution of Bernoulli(p=0.7) Distribution",
fontsize=16)
plt.xticks(np.arange(0, 2, 1))
plt.yticks(np.arange(0, 1.1, 0.1))
plt.legend(loc='best', shadow=True)
p = 0.7
print("Probability Mass Function = ", bernoulli.pmf(x, p))
#Plot the graph for Probability Mass Function(PMF):
x = [0, 1]
p = 0.7
plt.scatter(x, bernoulli.pmf(x, p), label="PMF")
plt.title("Probability Mass Function")
plt.xlabel("Data Points")
plt.ylabel("Probability")
plt.legend()
#Get Cumulative Density Function(CDF):
x = [0, 1]
p = 0.7
print("Cumulative Density Function = ", bernoulli.cdf(x, p))
#Plot the Cumulative Density Function(CDF):
x = [0, 1]
p = 0.7
plt.scatter(x, bernoulli.cdf(x, p), label="CDF")
plt.title("Cumulative Density Function")
plt.xlabel("Data Points")
plt.ylabel("Probability")
plt.legend()
#Plot the bar graph for PMF:
x = [0, 1]
p = 0.7
plt.bar(x, bernoulli.pmf(x, p), width=0.1, color=["r", "b"])
plt.title("Probability Mass Function")
from scipy.stats import bernoulli
import numpy as np
k = 3
p = 0.4
expect = bernoulli.expect(args=(p, ), loc=0)
mean = bernoulli.mean(p)
var = bernoulli.var(p)
sigma = bernoulli.std(p)
pmf = bernoulli.pmf(k, p, loc=0)
cdf = bernoulli.cdf(k, p, loc=0)
print('expected = ', expect)
print('mean = ', mean)
print('variance = ', var)
print('std. dev. = ', sigma)
print('pmf = ', pmf)
print('cdf = ', cdf)
def cdf(self, n, p):
cdf = bernoulli.cdf(self, n, p)
return cdf
from scipy.stats import bernoulli
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
p = 0.3
mean, var, skew, kurt = bernoulli.stats(p, moments='mvsk')
# Display the probability mass function (pmf):
x = np.arange(bernoulli.ppf(0.01, p),
bernoulli.ppf(0.99, p))
ax.plot(x, bernoulli.pmf(x, p), 'bo', ms=8, label='bernoulli pmf')
ax.vlines(x, 0, bernoulli.pmf(x, p), colors='b', lw=5, alpha=0.5)
# Freeze the distribution and display the frozen pmf:
rv = bernoulli(p)
ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
label='frozen pmf')
ax.legend(loc='best', frameon=False)
plt.show()
# Check accuracy of cdf and ppf:
prob = bernoulli.cdf(x, p)
np.allclose(x, bernoulli.ppf(prob, p))
# Generate random numbers:
r = bernoulli.rvs(p, size=1000)
def _cdf(self, p1):
cdf = bernoulli.cdf([0, 1], p1) * (1 << self.precision)
cdf = np.insert(np.around(cdf).astype(int), 0, 0)
# Prevent overflow.
cdf[1] = np.clip(cdf[1], 1, (1 << self.precision) - 1)
return cdf