利用python繪制正態分佈曲線

#-*-coding:utf-8-*-
"""
python繪制標準正態分佈曲線
"""
# ==============================================================
import numpy as np
import math
import matplotlib.pyplot as plt


def gd(x, mu=0, sigma=1):
  """根據公式，由自變量x計算因變量的值

  Argument:
    x: array
      輸入數據（自變量）
    mu: float
      均值
    sigma: float
      方差
  """
  left = 1 / (np.sqrt(2 * math.pi) * np.sqrt(sigma))
  right = np.exp(-(x - mu)**2 / (2 * sigma))
  return left * right


if __name__ == '__main__':
  # 自變量
  x = np.arange(-4, 5, 0.1)
  # 因變量（不同均值或方差）
  y_1 = gd(x, 0, 0.2)
  y_2 = gd(x, 0, 1.0)
  y_3 = gd(x, 0, 5.0)
  y_4 = gd(x, -2, 0.5)

  # 繪圖
  plt.plot(x, y_1, color='green')
  plt.plot(x, y_2, color='blue')
  plt.plot(x, y_3, color='yellow')
  plt.plot(x, y_4, color='red')
  # 設置坐標系
  plt.xlim(-5.0, 5.0)
  plt.ylim(-0.2, 1)

  ax = plt.gca()
  ax.spines['right'].set_color('none')
  ax.spines['top'].set_color('none')
  ax.xaxis.set_ticks_position('bottom')
  ax.spines['bottom'].set_position(('data', 0))
  ax.yaxis.set_ticks_position('left')
  ax.spines['left'].set_position(('data', 0))

  plt.legend(labels=['$\mu = 0, \sigma^2=0.2$', '$\mu = 0, \sigma^2=1.0$', '$\mu = 0, \sigma^2=5.0$', '$\mu = -2, \sigma^2=0.5$'])
  plt.show()