练习：均值、标准差、偏度、峰度的绘制

均值

标准差

偏度

峰度

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()