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 = 0.0niu2 = 0.0niu3 = 0.0for a in data:niu += aniu2 += a**2niu3 += a**3niu/= 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 = 0.0for a in data:a -= niuniu4 += a ** 4niu4 /= 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,kurtprint niu2,sigma2,skew2,kurt2print niu3,sigma3,skew3,kurt3print niu4,sigma4,skew4,kurt4info = 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()
