直方圖及分布曲線

直方圖可以大致查看數據分布是否為正態。通常還需要將正態分布的曲線疊加在上面。

導入需要的包

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

定義生成均值為mu，方差為sigma的正態分布對應y值的函數

def norm(x, mu, sigma):
    return ((1/(np.sqrt(2*np.pi)*sigma))*np.exp(-0.5*(1/sigma*(x-mu))**2))

生成測試數據

data = np.random.normal(size=100000)
mu = np.mean(data)
sigma = np.std(data)
num_bins = 100

繪制直方圖

fig, ax = plt.subplots()
# histogram
n, bins, patches = ax.hist(
                    data, 
                    bins=num_bins, 
                    density=True,
                    color='#2792C3')

添加正態分布的曲線

y = norm(bins, mu, sigma)
ax.plot(
    bins, 
    y,
    color='#EE827C',
    ls='--'
)

添加95%分位數線

tmp_thr = stats.norm.ppf(0.95)
thr = tmp_thr*sigma+mu
y_thr = norm(thr, mu, sigma)
ax.plot(
    [thr, thr],
    [0, y_thr],
    color='#EE827C',
    ls='--'
)

用顏色填充對應的區域。其中，zorder用來指定相應組塊的層數，即調整與其他組塊的重疊關系。

tmp_x = np.linspace(thr, np.max(data), num=100)
tmp_y = norm(tmp_x, mu, sigma)
ax.fill_between(tmp_x, 0, tmp_y, facecolor='#EE827C', zorder=2, alpha=0.5)

設置坐標軸標簽並保存圖片

ax.set_xlabel('Data')
ax.set_ylabel('Density')

plt.savefig('demo.pdf', bbox_inches='tight')

示例圖

完整代碼

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt

def norm(x, mu, sigma):
    return ((1/(np.sqrt(2*np.pi)*sigma))*np.exp(-0.5*(1/sigma*(x-mu))**2))

# generate the test data
data = np.random.normal(size=100000)
mu = np.mean(data)
sigma = np.std(data)
num_bins = 100

fig, ax = plt.subplots()
# histogram
n, bins, patches = ax.hist(
                    data, 
                    bins=num_bins, 
                    density=True,
                    color='#2792C3')

# normal distribution line
y = norm(bins, mu, sigma)
ax.plot(
    bins, 
    y,
    color='#EE827C',
    ls='--'
)

# add line of 95% quantile
tmp_thr = stats.norm.ppf(0.95)
thr = tmp_thr*sigma+mu
y_thr = norm(thr, mu, sigma)
ax.plot(
    [thr, thr],
    [0, y_thr],
    color='#EE827C',
    ls='--'
)

# fill the area greater than 95% quantile with color
tmp_x = np.linspace(thr, np.max(data), num=100)
tmp_y = norm(tmp_x, mu, sigma)
ax.fill_between(tmp_x, 0, tmp_y, facecolor='#EE827C', zorder=2, alpha=0.5)

ax.set_xlabel('Data')
ax.set_ylabel('Density')

# save fig
plt.savefig('demo.pdf', bbox_inches='tight')