In [1]:
theta = 0.6
rv = sp.stats.bernoulli(theta)
rv
Out[1]:
<scipy.stats._distn_infrastructure.rv_frozen at 0x7f76e93057d0>
In [4]:
xx = [0,1]
plt.bar(xx, rv.pmf(xx), align="center")
plt.xlim(-1, 2)
plt.ylim(0, 1)
plt.xticks([0, 1], ["X=0", "X=1"])
plt.ylabel("P(x)")
plt.title("pmf of Bernoulli distribution")
Out[4]:
<matplotlib.text.Text at 0x7f76e8c1c750>
In [5]:
coin = rv.rvs(100)
In [6]:
coin
Out[6]:
array([1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1,
1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0,
0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1,
1, 1, 0, 1, 1, 0, 1, 1])
In [14]:
countplt= sns.countplot(coin)
plt.show(countplt)
In [18]:
y = np.bincount(coin, minlength=2) / len(coin)
df = pd.DataFrame({"theoretic": rv.pmf(xx), "simulation" : y}).stack()
df = df.reset_index()
df.columns = ["value", "type", "ratio"]
df
Out[18]:
value
type
ratio
0
0
simulation
0.31
1
0
theoretic
0.40
2
1
simulation
0.69
3
1
theoretic
0.60
In [19]:
sns.barplot(x="value", y="ratio", hue = "type", data=df)
plt.show()
In [20]:
N = 10
theta = 0.6
rv = sp.stats.binom(N,theta)
rv
Out[20]:
<scipy.stats._distn_infrastructure.rv_frozen at 0x7f76e19dc390>
In [22]:
xx = np.arange(N + 1)
plt.bar(xx, rv.pmf(xx), align="center")
plt.ylabel("P(x)")
plt.title("pmf of binomial distribution")
plt.show()
In [23]:
np.random.seed(0)
x = rv.rvs(100)
x
Out[23]:
array([ 6, 5, 6, 6, 6, 5, 6, 4, 3, 6, 5, 6, 6, 4, 8, 8, 9,
5, 5, 4, 3, 5, 6, 5, 8, 5, 8, 4, 6, 6, 7, 5, 6, 6,
9, 6, 6, 6, 4, 5, 7, 6, 5, 8, 5, 5, 7, 8, 7, 7, 6,
6, 2, 8, 7, 8, 5, 7, 6, 7, 8, 8, 5, 8, 7, 7, 5, 8,
4, 8, 3, 6, 3, 6, 5, 9, 7, 8, 7, 8, 7, 6, 8, 5, 6,
7, 6, 8, 6, 4, 7, 5, 8, 5, 7, 7, 6, 9, 5, 10])
In [24]:
sns.countplot(x)
plt.show()
In [25]:
y = np.bincount(x, minlength=N) / len(x)
df = pd.DataFrame({"theoretic": rv.pmf(xx), "simulation" : y}).stack()
df = df.reset_index()
df.columns = ["value", "type", "ratio"]
df.head()
Out[25]:
value
type
ratio
0
0
simulation
0.000000
1
0
theoretic
0.000105
2
1
simulation
0.000000
3
1
theoretic
0.001573
4
2
simulation
0.010000
In [26]:
sns.barplot(x="value", y="ratio", hue="type", data = df)
plt.show()
In [32]:
a = np.arange(11)
rv.pmf([1,2,3])
Out[32]:
array([ 0.00157286, 0.01061683, 0.04246733])
In [35]:
rv.pmf?
In [38]:
np.random.seed(0)
x = np.random.randn(100)
plt.figure(figsize=(7,7))
sp.stats.probplot(x,plot=plt)
plt.axis("equal")
plt.show()
In [40]:
np.random.seed(0)
x = np.random.rand(100)
plt.figure(figsize=(7,7))
sp.stats.probplot(x,plot=plt)
plt.ylim(-0.5,1.5)
plt.show()
In [48]:
xx = np.linspace(-2, 2, 100)
plt.figure(figsize=(6,9))
for i, N in enumerate([1,2,30]):
X = np.random.rand(1000, N) - 0.5
S = X.sum(axis=1) / np.sqrt(N)
plt.subplot(3, 2, 2*i+1)
sns.distplot(S, bins=10, kde=False, norm_hist=True)
plt.xlim(-2,2)
plt.yticks([])
plt.subplot(3,2,2*i+2)
sp.stats.probplot(S, plot=plt)
plt.tight_layout()
plt.show()
In [46]:
Out[46]:
array([[ 5.48813504e-01],
[ 7.15189366e-01],
[ 6.02763376e-01],
[ 5.44883183e-01],
[ 4.23654799e-01],
[ 6.45894113e-01],
[ 4.37587211e-01],
[ 8.91773001e-01],
[ 9.63662761e-01],
[ 3.83441519e-01],
[ 7.91725038e-01],
[ 5.28894920e-01],
[ 5.68044561e-01],
[ 9.25596638e-01],
[ 7.10360582e-02],
[ 8.71292997e-02],
[ 2.02183974e-02],
[ 8.32619846e-01],
[ 7.78156751e-01],
[ 8.70012148e-01],
[ 9.78618342e-01],
[ 7.99158564e-01],
[ 4.61479362e-01],
[ 7.80529176e-01],
[ 1.18274426e-01],
[ 6.39921021e-01],
[ 1.43353287e-01],
[ 9.44668917e-01],
[ 5.21848322e-01],
[ 4.14661940e-01],
[ 2.64555612e-01],
[ 7.74233689e-01],
[ 4.56150332e-01],
[ 5.68433949e-01],
[ 1.87898004e-02],
[ 6.17635497e-01],
[ 6.12095723e-01],
[ 6.16933997e-01],
[ 9.43748079e-01],
[ 6.81820299e-01],
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[ 4.37031954e-01],
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[ 6.66766715e-01],
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[ 2.10382561e-01],
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In [47]:
np.random.seed(0)
np.random.rand(1000,1) - 0.5
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In [ ]:
Content source: rrbb014/fastcampus_dss
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