第七周作业-使用Python实现抽样分布的验证(正态分布、卡方分布、T分布等)

1.验证数据是否服从正态分布？

import pandas as pd
import numpy as np

path = 'E:\english\data.xlsx'
data=pd.read_excel(path)
######按照港口分类，计算数据的统计量
embark = data.groupby(['Embarked'])
embark_basic=data.groupby(['Embarked']).agg(['count','min','max','median','mean','var','std'])
age_basic=embark_basic['Age']
fare_basic=embark_basic['Fare']

age_basic
 count   min   max  median       mean         var        std
Embarked                                                             
C           130  0.42  71.0    29.0  30.814769  238.234892  15.434860
Q            28  2.00  70.5    27.0  28.089286  286.130622  16.915396
S           554  0.67  80.0    28.0  29.445397  200.029876  14.143192

fare_basic
	count	min	max	median	mean	var	std
Embarked							
C	130	4.0125	512.3292	36.2521	68.296767	8200.719153	90.557822
Q	28	6.7500	90.0000	7.7500	18.265775	477.142064	21.843582
S	554	0.0000	263.0000	13.0000	27.476284	1335.636543	36.546362

验证年龄是否服从正态分布

import seaborn as sns

sns.set_palette("hls")

sns.distplot(data['Age'],color='r',bins=10,kde=True)

plt.title('Age')

plt.xlim(-10,80)

plt.grid(True)

plt.show()
![](https://img2018.cnblogs.com/blog/1537138/201912/1537138-20191215212439759-713899714.png)

验证是否服从正态分布

from scipy import stats
ks_test = stats.kstest(data['Age'], 'norm')
shapiro_test=stats.shapiro(data['Age'])
normaltest_test=stats.normaltest(data['Age'],axis=0)

print('ks_test:',ks_test)
print('shapiro_test:',shapiro_test)
print('normaltest_test:',normaltest_test)
ks_test: KstestResult(statistic=0.9649422367998306, pvalue=0.0)

shapiro_test: (0.9815102219581604, 7.906476895414016e-08)
normaltest_test: NormaltestResult(statistic=18.12938011101228, pvalue=0.00011567916063448067)

由于p<0.05，拒绝原假设，认为数据不服从正态分布

绘制拟合正态分布曲线

age = data['Age']
plt.figure()
age.plot(kind = 'kde') ###### 原始数据的正态分布

M_S=stats.norm.fit(age) ######正态分布拟合的平均值loc，标准差 scale
normalDistribution = stats.norm(M_S[0], M_S[1]) ###### 绘制拟合的正态分布图
x = np.linspace(normalDistribution.ppf(0.01), normalDistribution.ppf(0.99), 100)
plt.plot(x, normalDistribution.pdf(x), c='orange')
plt.xlabel('Age about Titanic')
plt.title('Age on NormalDistribution', size=20)
plt.legend(['age', 'NormDistribution'])
![](https://img2018.cnblogs.com/blog/1537138/201912/1537138-20191215212727714-1302946705.png)

2验证是否服从T分布

np.random.seed(1)
ks = stats.t.fit(age)
df = ks[0]
loc = ks[1]
scale = ks[2]
ks2 = stats.t.rvs(df=df,loc=loc,scale=scale,size=len(age))
stats.ks_2samp(age,ks2)

p<0.05,拒绝原假设，认为数据不服从T分布

绘制拟合的T分布图

plt.figure()
age.plot(kind = 'kde')
TDistribution = stats.t(ks[0],ks[1],ks[2])
x = np.linspace(TDistribution.ppf(0.01), TDistribution.ppf(0.99), 100)
plt.plot(x, TDistribution.pdf(x),c='orange')
plt.xlabel('age about Titanic')
plt.title('age on TDistribution',size=20)
plt.legend(['age','TDistribution'])
![](https://img2018.cnblogs.com/blog/1537138/201912/1537138-20191215212827653-310406875.png)

3.验证数据是否服从卡方分布

chi_S = stats.chi2.fit(age)
df_chi = chi_S[0]
loc_chi = chi_S[1]
scale_chi = chi_S[2]
chi2 = stats.chi2.rvs(df=df_chi,loc=loc_chi,scale=scale_chi,size=len(age))
stats.ks_2samp(age,chi2)

Ks_2sampResult(statistic=0.05898876404494382, pvalue=0.1678541416784373)

对数据进行卡方拟合

plt.figure()
age.plot(kind='kde')
chiDistribution=stats.chi2(chi_S[0],chi_S[1],chi_S[2]) # 绘制拟合的正态分布图
x=np.linspace(chiDistribution.ppf(0.01),chiDistribution.ppf(0.99),100)
plt.plot(x,chiDistribution.pdf(x),c='orange')
plt.xlabel('age about Titanic')
plt.title('age on chi-square_Distribution', size=20)
plt.legend(['age','chi-square_Distribution'])
![](https://img2018.cnblogs.com/blog/1537138/201912/1537138-20191215212919939-2044472972.png)