import numpy as np

from scipy import stats

import math

import matplotlib as mpl

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import Axes3D

from matplotlib import cm

# import seaborn

def calc_statistics(x):

n = x.shape[0] # 样本个数

# 手动计算

m = 0

m2 = 0

m3 = 0

m4 = 0

for t in x:

m += t

m2 += t*t

m3 += t**3

m4 += t**4

m /= n

m2 /= n

m3 /= n

m4 /= n

#参考上面的偏度峰度公式

mu = m

sigma = np.sqrt(m2 - mu*mu)

skew = (m3 - 3*mu*m2 + 2*mu**3) / sigma**3

kurtosis = (m4 - 4*mu*m3 + 6*mu*mu*m2 - 4*mu**3*mu + mu**4) / sigma**4 - 3

print('手动计算均值、标准差、偏度、峰度：', mu, sigma, skew, kurtosis)

# 使用系统函数验证

mu = np.mean(x, axis=0)

sigma = np.std(x, axis=0)

skew = stats.skew(x)

kurtosis = stats.kurtosis(x)

return mu, sigma, skew, kurtosis

if __name__ == '__main__':

d = np.random.randn(10000)

print(d)

print(d.shape)

mu, sigma, skew, kurtosis = calc_statistics(d)

print('函数库计算均值、标准差、偏度、峰度：', mu, sigma, skew, kurtosis)

# 一维直方图

mpl.rcParams['font.sans-serif'] = 'SimHei'

mpl.rcParams['axes.unicode_minus'] = False

plt.figure(num=1, facecolor='w')

y1, x1, dummy = plt.hist(d, bins=50, normed=True, color='g', alpha=0.75, edgecolor='k')

t = np.arange(x1.min(), x1.max(), 0.05)

y = np.exp(-t**2 / 2) / math.sqrt(2*math.pi)

plt.plot(t, y, 'r-', lw=2)

plt.title('高斯分布，样本个数：%d' % d.shape[0])

plt.grid(True)

# plt.show()

d = np.random.randn(100000, 2)

mu, sigma, skew, kurtosis = calc_statistics(d)

print('函数库计算均值、标准差、偏度、峰度：', mu, sigma, skew, kurtosis)

# 二维图像

N = 30

density, edges = np.histogramdd(d, bins=[N, N])

print('样本总数：', np.sum(density))

density /= density.max()

x = y = np.arange(N)

print('x = ', x)

print('y = ', y)

t = np.meshgrid(x, y)

print(t)

fig = plt.figure(facecolor='w')

ax = fig.add_subplot(111, projection='3d')

ax.scatter(t[0], t[1], density, c='r', s=50*density, marker='o', depthshade=True)

ax.plot_surface(t[0], t[1], density, cmap=cm.Accent, rstride=1, cstride=1, alpha=0.9, lw=0.75, edgecolor='k')

ax.set_xlabel('X')

ax.set_ylabel('Y')

ax.set_zlabel('Z')

plt.title('二元高斯分布，样本个数：%d' % d.shape[0], fontsize=15)

plt.tight_layout(0.1)

plt.show()