import numpy as np
import pandas as pd
%matplotlib inline
import matplotlib
import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus']=False
#导入模块

# 直方图判断

s = pd.DataFrame(np.random.randn(1000)+10,columns = ['values'])
print(s.head())

fig = plt.figure(figsize = (10,6))
ax1 = fig.add_subplot(2,1,1)
ax1.scatter(s.index,s.values,color = 'blue',edgecolor = 'black')
plt.xlim([-200,1200])
plt.ylim([6,15])
plt.yticks(range(6,16))
plt.grid(True,linestyle = '--')

ax2 = fig.add_subplot(2,1,2)
s.hist(bins = 30,alpha = 0.5,color = 'blue',edgecolor = 'black',ax = ax2)
plt.xlim([2,18])
plt.ylim([0,100])
s.plot(kind = 'kde',secondary_y = True,color = 'g',ax = ax2)
plt.grid(True,linestyle = '--')

# QQ图判断
# QQ图通过把测试样本数据的分位数与已知分布相比较，从而来检验数据的分布情况

# QQ图是一种散点图，对应于正态分布的QQ图，就是由标准正态分布的分位数为横坐标，样本值为纵坐标的散点图
# 参考直线：四分之一分位点和四分之三分位点这两点确定，看散点是否落在这条线的附近

# 绘制思路
# ① 在做好数据清洗后，对数据进行排序（次序统计量：x(1)<x(2)<....<x(n)）
# ② 排序后，计算出每个数据对应的百分位p{i}，即第i个数据x(i)为p(i)分位数，其中p(i)=(i-0.5)/n （pi有多重算法，这里以最常用方法为主）
# ③ 绘制直方图 + qq图，直方图作为参考

s = pd.DataFrame(np.random.randn(1000)+10,columns = ['value'])
print(s.head())

mean = s['value'].mean()
std = s['value'].std()
print('均值为：%.2f,标准差为：%.2f' % (mean,std))
print('---------------')

s.sort_values(by = 'value',inplace = True)
s_r = s.reset_index(drop = False)
s_r['p'] = (s_r.index - 0.5)/len(s_r)
s_r['q'] = (s_r['value']-mean)/std
print(s_r.head())
print('-------------')

st = s['value'].describe()
print(st)
x1,y1 = 0.25,st['25%']
x2,y2 = 0.75,st['75%']
print('四分之一位数为：%.2f，四分之三位数为：%.2f' % (y1,y2))
print('------')

fig = plt.figure(figsize = (10,9))
ax1 = fig.add_subplot(3,1,1)
ax1.scatter(s.index,s.value,color = 'b',edgecolor = 'k')
plt.grid(True,linestyle = '--')

ax2 = fig.add_subplot(3,1,2)
s.hist(bins = 30,alpha = 0.5,color = 'b',edgecolor = 'k',ax = ax2)
s.plot(kind = 'kde',color = 'g',secondary_y = True,ax = ax2)
plt.grid(True,linestyle = '--')

ax3 = fig.add_subplot(3,1,3)
ax3.plot(s_r['p'],s_r['value'],color = 'k',alpha = 0.8)
ax3.plot([x1,x2],[y1,y2],'-r')
plt.grid()

# KS检验，理论推导

data = [87,77,92,68,80,78,84,77,81,80,80,77,92,86,
       76,80,81,75,77,72,81,72,84,86,80,68,77,87,
       76,77,78,92,75,80,78]
# 样本数据，35位健康男性在未进食之前的血糖浓度

df = pd.DataFrame(data, columns =['value'])
u = df['value'].mean()
std = df['value'].std()
print("样本均值为：%.2f，样本标准差为：%.2f" % (u,std))
print('------')
# 查看数据基本统计量

s = df['value'].value_counts().sort_index()
df_s = pd.DataFrame({'血糖浓度':s.index,'次数':s.values})
# 创建频率数据

df_s['累计次数'] = df_s['次数'].cumsum()
df_s['累计频率'] = df_s['累计次数'] / len(data)
df_s['标准化取值'] = (df_s['血糖浓度'] - u) / std
df_s['理论分布'] =[0.0244,0.0968,0.2148,0.2643,0.3228,0.3859,0.5160,0.5832,0.7611,0.8531,0.8888,0.9803]  # 通过查阅正太分布表
df_s['D'] = np.abs(df_s['累计频率'] - df_s['理论分布'])
dmax = df_s['D'].max()
print("实际观测D值为：%.4f" % dmax)
# D值序列计算结果表格

df_s['累计频率'].plot(style = '--k.')
df_s['理论分布'].plot(style = '--r.')
plt.legend(loc = 'upper left')
plt.grid()
# 密度图表示

df_s

# 直接用算法做KS检验

from scipy import stats
# scipy包是一个高级的科学计算库，它和Numpy联系很密切，Scipy一般都是操控Numpy数组来进行科学计算

data = [87,77,92,68,80,78,84,77,81,80,80,77,92,86,
       76,80,81,75,77,72,81,72,84,86,80,68,77,87,
       76,77,78,92,75,80,78]
# 样本数据，35位健康男性在未进食之前的血糖浓度

df = pd.DataFrame(data, columns =['value'])
u = df['value'].mean()  # 计算均值
std = df['value'].std()  # 计算标准差
stats.kstest(df['value'], 'norm', (u, std))
# .kstest方法：KS检验，参数分别是：待检验的数据，检验方法（这里设置成norm正态分布），均值与标准差
# 结果返回两个值：statistic → D值，pvalue → P值
# p值大于0.05，为正态分布

from scipy import stats
data = [87,77,92,68,80,78,84,77,81,80,80,77,92,86,
       76,80,81,75,77,72,81,72,84,86,80,68,77,87,
       76,77,78,92,75,80,78]
df = pd.DataFrame(data,columns = ['value'])
u = df['value'].mean()
std = df['value'].std()
stats.kstest(df['value'],'norm',(u,std))