计算偏度Skewness与峰度kurtosis的python程序——简单

偏度和峰度都是统计量
偏度Skewness(三阶) ——三阶中心距除以标准差的三次方

峰度Kurtosis (四阶) —— 概率密度在均值处峰值高低的特征，常定义四阶中心矩除以方差的平方，减去三；

import matplotlib.pyplot as pltimport mathimport numpy as npdef calc(data):    n = len(data)    niu = 0.0    niu2 = 0.0    niu3 = 0.0    for a in data:        niu += a        niu2 += a**2        niu3 += a**3    niu/= n   #这是求E(X)    niu2 /= n #这是E(X^2)    niu3 /= n #这是E(X^3)    sigma = math.sqrt(niu2 - niu*niu) #这是D（X）的开方，标准差    return [niu,sigma,niu3] #返回[E（X）,标准差，E（X^3）]def calc_stat(data):    [niu,sigma,niu3] = calc(data)    n = len(data)    niu4 = 0.0    for a in data:        a -= niu        niu4 += a ** 4    niu4 /= n       skew = (niu3 - 3*niu*sigma**2 - niu**3)/(sigma**3)    kurt =  niu4/(sigma**2)    return [niu,sigma,skew,kurt] #返回了均值，标准差，偏度，峰度if __name__== "__main__":    data = list(np.random.randn(10000))#关于此处的数组与列表    data2 = list(2*np.random.randn(10000))    data3 = [x for x in data if x> -0.5]    data4 = list(np.random.uniform(0,4,10000))    [niu,sigma,skew,kurt] = calc_stat(data)    [niu2,sigma2,skew2,kurt2] = calc_stat(data2)    [niu3,sigma3,skew3,kurt3] = calc_stat(data3)    [niu4,sigma4,skew4,kurt4] = calc_stat(data4)    print niu,sigma,skew,kurt    print niu2,sigma2,skew2,kurt2    print niu3,sigma3,skew3,kurt3    print niu4,sigma4,skew4,kurt4    info = r'$\mu=%.2f,\ \sigma=%.2f,\ skew=%.2f,\ kurt=%.2f$'%(niu,sigma,skew,kurt)    info2 =r'$\mu=%.2f,\ \sigma=%.2f,\ skew=%.2f,\ kurt=%.2f$'%(niu2,sigma2,skew2,kurt2)    plt.text(1,0.38,info,bbox=dict(facecolor='red',alpha=0.25))    plt.text(1,0.35,info2,bbox=dict(facecolor='green',alpha=0.25))    #plt.text(x的位置，y的位置，面板内写的信息，标签框的属性=dict（facecolor='面板颜色'，alpha='深浅度'）)    plt.hist(data,50,normed=True,facecolor='r',alpha=0.9)    #hist直方图/箱式图(    #将data中的元素分到50个等间隔的范围内，返回每个范围内元素的个数作为一个行向量，    #50代表要分的元素的个数    #    #facecolor,alpha都是代表颜色的)    plt.hist(data2,80,normed=True,facecolor='g',alpha = 0.8)    plt.grid(True)    plt.show()