Python繪制正態分布曲線

  使用Python繪制正態分布曲線，借助matplotlib繪圖工具；

\[f(x) = \dfrac{1}{\sqrt{2\pi}\sigma}\exp(-\dfrac{(x-\mu)^2}{2\sigma^2}) \]

#-*-coding:utf-8-*-
"""
python繪制標准正態分布曲線
"""
# ==============================================================
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()