def plot(self):
p = 0.5
mean, var, skew, kurt = geom.stats(p, moments='mvsk')
x = np.arange(geom.ppf(0.01, p), geom.ppf(0.99, p))
ax.plot(x, geom.pmf(x, p), 'bo', ms=8, label='geom pmf')
ax.vlines(x, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5)
rv = geom(p)
ax.vlines(x,
0,
rv.pmf(x),
colors='k',
linestyles='-',
lw=1,
label='frozen pmf')
ax.legend(loc='best', frameon=False)
plt.show()
def test_geom(self):
from scipy.stats import geom
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
p = 0.5
mean, var, skew, kurt = geom.stats(p, moments='mvsk')
x = np.arange(geom.ppf(0.01, p), geom.ppf(0.99, p))
ax.plot(x, geom.pmf(x, p), 'bo', ms=8, label='geom pmf')
ax.vlines(x, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5)
rv = geom(p)
ax.vlines(x,
0,
rv.pmf(x),
colors='k',
linestyles='-',
lw=1,
label='frozen pmf')
ax.legend(loc='best', frameon=False)
self.assertEqual(str(ax), "AxesSubplot(0.125,0.11;0.775x0.77)")
def test_geometric_max_draw_list(self, n, p, maxv):
"""
NB: slight mismatches on arrays possibly due to rounding error in C
"""
array_c = covid19.intArray(n)
covid19.geometric_max_draw_list(array_c, n, p, maxv)
array_c = np.array(c_array_as_python_list(array_c, n))
array_np = geom.ppf(np.linspace(1 / n, 1 - 1 / n, n), p) - 1
array_np = np.minimum(array_np, maxv)
np.testing.assert_almost_equal(np.mean(array_c),
np.mean(array_np),
decimal=2)
def generate_graph_data(self):
ageGroup = self.tableModel.data[self.selected_item_index.row()][0]
parameter = self.tableModel.data[self.selected_item_index.row()][1]
p1 = self.temporaryParametersDict[ageGroup][parameter]["p1"]
p2 = self.temporaryParametersDict[ageGroup][parameter]["p2"]
distributionType = self.temporaryParametersDict[ageGroup][parameter][
"distributionType"]
xyDict = {"x": [], "y": []}
try:
if distributionType == 'Binomial':
xyDict["x"] = np.arange(binom.ppf(0.01, int(p1), p2 / 100),
binom.ppf(0.99, int(p1), p2 / 100))
xyDict["y"] = binom.pmf(xyDict["x"], int(p1), p2 / 100)
elif distributionType == 'Geometric':
xyDict["x"] = np.arange(geom.ppf(0.01, p1 / 100),
geom.ppf(0.99, p1 / 100))
xyDict["y"] = geom.pmf(xyDict["x"], p1 / 100)
if p2 != 0:
self.tableModel.setData(
self.selected_item_index.sibling(
self.selected_item_index.row(), 3), 0, Qt.EditRole)
elif distributionType == 'Laplacian':
xyDict["x"] = np.arange(dlaplace.ppf(0.01, p1 / 100),
dlaplace.ppf(0.99, p1 / 100))
xyDict["y"] = dlaplace.pmf(xyDict["x"], p1 / 100)
if p2 != 0:
self.tableModel.setData(
self.selected_item_index.sibling(
self.selected_item_index.row(), 3), 0, Qt.EditRole)
elif distributionType == 'Logarithmic':
xyDict["x"] = np.arange(logser.ppf(0.01, p1 / 100),
logser.ppf(0.99, p1 / 100))
xyDict["y"] = logser.pmf(xyDict["x"], p1 / 100)
if p2 != 0:
self.tableModel.setData(
self.selected_item_index.sibling(
self.selected_item_index.row(), 3), 0, Qt.EditRole)
elif distributionType == 'Neg. binomial':
xyDict["x"] = np.arange(nbinom.ppf(0.01, p1, p2 / 100),
nbinom.ppf(0.99, p1, p2 / 100))
xyDict["y"] = nbinom.pmf(xyDict["x"], p1, p2 / 100)
elif distributionType == 'Planck':
xyDict["x"] = np.arange(planck.ppf(0.01, p1 / 100),
planck.ppf(0.99, p1 / 100))
xyDict["y"] = planck.pmf(xyDict["x"], p1 / 100)
if p2 != 0:
self.tableModel.setData(
self.selected_item_index.sibling(
self.selected_item_index.row(), 3), 0, Qt.EditRole)
elif distributionType == 'Poisson':
xyDict["x"] = np.arange(poisson.ppf(0.01, p1),
poisson.ppf(0.99, p1))
xyDict["y"] = poisson.pmf(xyDict["x"], p1)
if p2 != 0:
self.tableModel.setData(
self.selected_item_index.sibling(
self.selected_item_index.row(), 3), 0, Qt.EditRole)
elif distributionType == 'Uniform':
if p1 - 0.5 * p2 < 0:
p2 = p1
min = p1 - 0.5 * p2
max = p1 + 0.5 * p2
xyDict["x"] = np.arange(randint.ppf(0.01, min, max),
randint.ppf(0.99, min, max))
xyDict["y"] = randint.pmf(xyDict["x"], min, max)
elif distributionType == 'Zipf (Zeta)':
xyDict["x"] = np.arange(zipf.ppf(0.01, p1), zipf.ppf(0.99, p1))
xyDict["y"] = zipf.pmf(xyDict["x"], p1)
if p2 != 0:
self.tableModel.setData(
self.selected_item_index.sibling(
self.selected_item_index.row(), 3), 0, Qt.EditRole)
self.update_graph(xyDict)
except Exception as E:
log.error(E)
rv = nbinom(n, p) ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, label='frozen pmf') ax.legend(loc='best', frameon=False) # ============================================= # # ================= GEOMETRIQUE =============== # # ============================================= # fig, ax = plt.subplots(1, 1) p = 0.3 mean, var, skew, kurt = geom.stats(p, moments='mvsk') x = np.arange(geom.ppf(0.01, p), geom.ppf(0.99, p)) ax.plot(x, geom.pmf(x, p), 'bo', ms=8, label='geom pmf') ax.vlines(x, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5) rv = geom(p) ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1, label='frozen pmf') ax.legend(loc='best', frameon=False) # ============================================= # # =================== POISSON ================= # # ============================================= # fig, ax = plt.subplots(1, 1) mu = 20
plt.title("Cumulative Density Function of Binomial(n=10,p=0.4) Distribution",
fontsize=16)
plt.xticks(np.arange(-2, 9, 1))
plt.yticks(np.arange(0, 1.1, 0.1))
plt.legend(loc='upper left', shadow=True)
plt.show()
# ### Geometric Distribution
# In[4]:
#Geometric Distribution
from scipy.stats import geom
p = 0.6
x = np.arange(geom.ppf(0.01, p), geom.ppf(
0.99, p)) #Percent Point Function (inverse of cdf — percentiles)
print("Mean : ", geom.stats(p, moments='m'))
print("Variance : ", geom.stats(p, moments='v'))
print("Prob. Mass Func. : ", geom.pmf(x, p))
print("Cum. Density Func.: ", geom.cdf(x, p))
CDF = geom.cdf(x, p)
fig = plt.figure(figsize=(20, 10))
plt.subplot(221)
plt.plot(x, geom.pmf(x, p), 'go', ms=8, label='PMF')
plt.vlines(x, 0, geom.pmf(x, p), colors='g', lw=5, alpha=0.5)
plt.xlabel("Sample Space of Geometric Distribution", fontsize=14)
plt.ylabel("PMF", fontsize=14)
from scipy.stats import geom
import matplotlib.pyplot as plt
fig, ax = plt.subplots(1, 1)
# Calculate a few first moments:
p = 0.5
mean, var, skew, kurt = geom.stats(p, moments='mvsk')
# Display the probability mass function (``pmf``):
x = np.arange(geom.ppf(0.01, p), geom.ppf(0.99, p))
ax.plot(x, geom.pmf(x, p), 'bo', ms=8, label='geom pmf')
ax.vlines(x, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5)
# Alternatively, the distribution object can be called (as a function)
# to fix the shape and location. This returns a "frozen" RV object holding
# the given parameters fixed.
# Freeze the distribution and display the frozen ``pmf``:
rv = geom(p)
ax.vlines(x,
0,
rv.pmf(x),
colors='k',
linestyles='-',
lw=1,
label='frozen pmf')
ax.legend(loc='best', frameon=False)
plt.show()
import numpy as np from scipy.stats import geom import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1) p = 0.5 mean, var, skew, kurt = geom.stats(p, moments='mvsk') x = np.arange(geom.ppf(0.01, p),geom.ppf(0.99, p)) ax.plot(x, geom.pmf(x, p), 'bo', ms=8, label='geom pmf') ax.vlines(x, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5) plt.show()
def testGeom(): # {{{
"""
Geometric Distribution (discrete)
Notes
-----
伯努利事件进行k次, 第一次成功的概率
为什么是几何分布呢, 为什么不叫几毛分布?
与几何数列有关 (乘积倍数)
p: 成功的概率
q: 失败的概率(1-p)
k: 第一次成功时的经历的次数 (前k-1次是失败的)
geom.pmf(k, p), (1-p)**(k-1)*p)
"""
# 准备数据: 已知 p.
# X轴: 第k次才成功
# Y轴: 概率
p = 0.4
xs = np.arange(geom.ppf(0.01, p), geom.ppf(0.99, p), step=1)
# E(X) = 1/p, D(X) = (1-p)/p**2
mean, var, skew, kurt = geom.stats(p, moments='mvsk')
print("mean: %.2f, var: %.2f, skew: %.2f, kurt: %.2f" %
(mean, var, skew, kurt))
fig, axs = plt.subplots(2, 2)
# 显示pmf1
ys = geom.pmf(xs, p)
axs[0][0].plot(xs, ys, 'bo', markersize=5, label='geom pmf')
axs[0][0].vlines(xs,
0,
ys,
colors='b',
linewidth=5,
alpha=0.5,
label='vline pmf')
axs[0][0].legend(loc='best', frameon=False)
# 显示pmf2
ys = (1 - p)**(xs - 1) * p
axs[0][1].plot(xs, ys, 'bo', markersize=5, label='geom pmf')
axs[0][1].vlines(xs,
0,
ys,
colors='b',
linewidth=5,
alpha=0.5,
label='vline pmf')
axs[0][1].legend(loc='best', frameon=False)
axs[0][1].set_title('ys = (1-p)**(xs-1)*p')
# 显示cdf P(X<=x)
ys = geom.cdf(xs, p)
axs[1][0].plot(xs, ys, 'bo', markersize=5, label='geom cdf')
axs[1][0].legend(loc='best', frameon=False)
print(np.allclose(xs, geom.ppf(ys, p))) # ppf:y-->x cdf:x-->y
# 生成随机数据(random variables)
data = geom.rvs(p, size=1000)
import sys
sys.path.append("../../thinkstats")
import Pmf
pmf = Pmf.MakePmfFromList(data)
xs, ys = pmf.Render()
axs[1][1].plot(xs, ys, 'bo', markersize=5, label='rvs-pmf')
plt.show()