#!/usr/bin/python
#??-*-?coding:utf-8?-*-

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


def?calc_statistics（x）:
????n?=?x.shape[0]??#?樣本個數(shù)
????#?手動計算
????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

????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?（‘手動計算均值、標(biāo)準(zhǔn)差、偏度、峰度：‘?mu?sigma?skew?kurtosis）

????#?使用系統(tǒng)函數(shù)驗證
????mu?=?np.mean（x?axis=0）?#求均值
????sigma?=?np.std（x?a