import pandas as pd
df = pd.read_excel('/Users/Downloads/data.xlsx',usecols = [1,2,3] )
#拿到港口'Embarked'、年龄'Age'、价格'Fare'的数据
df2 = df.groupby(['Embarked'])
#按照港口'Embarked'分类后，查看 年龄、车票价格的统计量。
# 变异系数 = 标准差/平均值
def cv(data):
  return data.std()/data.var()

df2 = df.groupby(['Embarked']).agg(['count','min','max','median','mean','var','std',cv])
df2 = df2.apply(lambda x:round(x,2))
df2_age = df2['Age']
df2_fare = df2['Fare']

plt.hist(df['Fare'],20,normed=1, alpha=0.75)
plt.title('Fare')
plt.grid(True)

#分别用kstest、shapiro、normaltest来验证分布系数
ks_test = kstest(df['Fare'], 'norm')
#KstestResult(statistic=0.99013849978633, pvalue=0.0)

shapiro_test = shapiro(df['Fare'])
#shapiroResult(0.5256513357162476, 7.001769945799311e-40)

normaltest_test = normaltest(df['Fare'],axis=0) 
#NormaltestResult(statistic=715.0752414548335, pvalue=5.289130045259168e-156)

fare = df['Fare']

plt.figure()
fare.plot(kind = 'kde')   #原始数据的正态分布

M_S = stats.norm.fit(fare)  #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('Fare about Titanic')
plt.title('Titanic[Fare] on NormalDistribution', size=20)
plt.legend(['Origin', 'NormDistribution'])

T_S = stats.t.fit(fare)
df = T_S[0] 
loc = T_S[1] 
scale = T_S[2] 
x2 = stats.t.rvs(df=df, loc=loc, scale=scale, size=len(fare))
D, p = stats.ks_2samp(fare, x2) # (0.25842696629213485 2.6844476044528504e-21)

plt.figure()
fare.plot(kind = 'kde') 
TDistribution = stats.t(T_S[0], T_S[1],T_S[2])  # 绘制拟合的T分布图
x = np.linspace(TDistribution.ppf(0.01), TDistribution.ppf(0.99), 100)
plt.plot(x, TDistribution.pdf(x), c='orange')
plt.xlabel('Fare about Titanic')
plt.title('Titanic[Fare] on TDistribution', size=20)
plt.legend(['Origin', 'TDistribution'])

chi_S = stats.chi2.fit(fare)
df_chi = chi_S[0] 
loc_chi = chi_S[1] 
scale_chi = chi_S[2] 
x2 = stats.chi2.rvs(df=df_chi, loc=loc_chi, scale=scale_chi, size=len(fare))
Df, pf = stats.ks_2samp(fare, x2) # (0.16292134831460675, 1.154755913291936e-08)

plt.figure()
fare.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('Fare about Titanic')
plt.title('Titanic[Fare] on chi-square_Distribution', size=20)
plt.legend(['Origin', 'chi-square_Distribution'])

S_fare = df[df['Embarked'] =='S']['Fare']
Q_fare = df[df['Embarked'] =='Q']['Fare']
C_fare = df[df['Embarked'] =='C']['Fare']
S_fare.describe()
count  554.000000
mean   27.476284
std    36.546362
min    0.000000
25%    8.050000
50%    13.000000
75%    27.862500
max   263.000000
Q_fare.describe()
count  28.000000
mean   18.265775
std   21.843582
min    6.750000
25%    7.750000
50%    7.750000
75%   18.906250
max   90.000000
C_fare.describe()
count  130.000000
mean   68.296767
std    90.557822
min    4.012500
25%    14.454200
50%    36.252100
75%    81.428100
max   512.329200

miu = np.mean(S_fare) - np.mean(C_fare)
sig = np.sqrt(np.var(S_fare, ddof=1)/len(S_fare) + np.var(C_fare, ddof=1)/len(C_fare))

x = np.arange(- 110, 50)
y = stats.norm.pdf(x, miu, sig)
plt.plot(x, y)
plt.xlabel("S_Fare - C_Fare")
plt.ylabel("Density")
plt.title('Fare difference between S and C')
plt.show()