均匀分布
import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
# for continuous
a =
b = 50
size = 5000
X_continuous = np.linspace(a, b, size)
continuous_uniform = stats.uniform(loc=a, scale=b)
continuous_uniform_pdf = continuous_uniform.pdf(X_continuous)
# for discrete
X_discrete = np.arange(1, 7)
discrete_uniform = stats.randint(1, 7)
discrete_uniform_pmf = discrete_uniform.pmf(X_discrete)
# plot both tables
fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(15,5))
# discrete plot
ax[].bar(X_discrete, discrete_uniform_pmf)
ax[].set_xlabel("X")
ax[].set_ylabel("Probability")
ax[].set_title("Discrete Uniform Distribution")
# continuous plot
ax[1].plot(X_continuous, continuous_uniform_pdf)
ax[1].set_xlabel("X")
ax[1].set_ylabel("Probability")
ax[1].set_title("Continuous Uniform Distribution")
plt.show()
高斯分布
mu =
variance = 1
sigma = np.sqrt(variance)
x = np.linspace(mu - 3*sigma, mu + 3*sigma, 100)
plt.subplots(figsize=(8, 5))
plt.plot(x, stats.norm.pdf(x, mu, sigma))
plt.title("Normal Distribution")
plt.show()
68% 的数据落在平均值的一个标准差内。 95% 的数据落在平均值的两个标准差内。 99.7% 的数据落在平均值的三个标准差范围内。
对数正态分布
X = np.linspace(, 6, 500)
std = 1
mean =
lognorm_distribution = stats.lognorm([std], loc=mean)
lognorm_distribution_pdf = lognorm_distribution.pdf(X)
fig, ax = plt.subplots(figsize=(8, 5))
plt.plot(X, lognorm_distribution_pdf, label="μ=0, σ=1")
ax.set_xticks(np.arange(min(X), max(X)))
std = 0.5
mean =
lognorm_distribution = stats.lognorm([std], loc=mean)
lognorm_distribution_pdf = lognorm_distribution.pdf(X)
plt.plot(X, lognorm_distribution_pdf, label="μ=0, σ=0.5")
std = 1.5
mean = 1
lognorm_distribution = stats.lognorm([std], loc=mean)
lognorm_distribution_pdf = lognorm_distribution.pdf(X)
plt.plot(X, lognorm_distribution_pdf, label="μ=1, σ=1.5")
plt.title("Lognormal Distribution")
plt.legend()
plt.show()
泊松分布
from scipy import stats
print(stats.poisson.pmf(k=9, mu=3))
0.002700503931560479
X = stats.poisson.rvs(mu=3, size=500)
plt.subplots(figsize=(8, 5))
plt.hist(X, density=True, edgecolor="black")
plt.title("Poisson Distribution")
plt.show()
指数分布
X = np.linspace(, 5, 5000)
exponetial_distribtuion = stats.expon.pdf(X, loc=, scale=1)
plt.subplots(figsize=(8,5))
plt.plot(X, exponetial_distribtuion)
plt.title("Exponential Distribution")
plt.show()
二项分布
P = 二项分布概率 = 组合数 x = n次试验中特定结果的次数 p = 单次实验中，成功的概率 q = 单次实验中，失败的概率 n = 实验的次数
X = np.random.binomial(n=1, p=0.5, size=1000)
plt.subplots(figsize=(8, 5))
plt.hist(X)
plt.title("Binomial Distribution")
plt.show()
学生 t 分布
import seaborn as sns
from scipy import stats
X1 = stats.t.rvs(df=1, size=4)
X2 = stats.t.rvs(df=3, size=4)
X3 = stats.t.rvs(df=9, size=4)
plt.subplots(figsize=(8,5))
sns.kdeplot(X1, label = "1 d.o.f")
sns.kdeplot(X2, label = "3 d.o.f")
sns.kdeplot(X3, label = "6 d.o.f")
plt.title("Student's t distribution")
plt.legend()
plt.show()
卡方分布
X = np.arange(, 6, 0.25)
plt.subplots(figsize=(8, 5))
plt.plot(X, stats.chi2.pdf(X, df=1), label="1 d.o.f")
plt.plot(X, stats.chi2.pdf(X, df=2), label="2 d.o.f")
plt.plot(X, stats.chi2.pdf(X, df=3), label="3 d.o.f")
plt.title("Chi-squared Distribution")
plt.legend()
plt.show()
原文链接：https://mp.weixin.qq.com/s/9k9hEqpM-N4yU_hxkVjfxw
