from scipy.stats import chi2 # 卡方分布
from scipy.stats import norm # 正態(tài)分布
from scipy.stats import t # t分布
from scipy.stats import f # F分布
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import scipy.stats as stats
from scipy.stats import chi2_contingency # 列聯(lián)表分析
# matplotlib畫圖注釋中文需要設(shè)置
from matplotlib.font_manager import FontProperties
xy_font_set = FontProperties(fname=r"c:\windows\fonts\方正稚藝簡體.ttf", size=12)
zhushi_font_set = FontProperties(fname=r"c:\windows\fonts\方正粗倩簡體.ttf", size=12)
titleYW_font_set = FontProperties(fname=r"c:\windows\fonts\Gabriola.ttf", size=20)
titleZW_font_set = FontProperties(fname=r"c:\windows\fonts\漢儀細(xì)行楷簡.ttf", size=18)
# rvs: Random Variates
# pdf: Probability Density Function 概率密度函數(shù)
# cdf: Cumulative Distribution Function 概率密度函數(shù)的積分函數(shù)
# sf: Survival Function (1-CDF)
# ppf: Percent Point Function (Inverse of CDF) 百分點(diǎn)函數(shù)，概率密度函數(shù)的積分值
# isf: Inverse Survival Function (Inverse of SF)
# stats: Return mean, variance, (Fisher’s) skew, or (Fisher’s) kurtosis
# moment: non-central moments of the distribution
# ppf以概率的形式，查詢函數(shù)值-----------類似分布臨界表
plt.figure()
# example ------------------------------------------- 卡方分布(右側(cè)單邊)
plt.subplot2grid((2, 2), (0, 0))
df = 20 # 自由度
# print(chi2.ppf(0.01, df)) # 計算函q=0.01概率時數(shù)值。其中 q = 1-a
# print(chi2.cdf(8.260, df)) # 知道x值求a
x = np.linspace(chi2.ppf(0.01, df), # 繪制概率密度圖
chi2.ppf(0.99, df), 100)
plt.plot(x, chi2.pdf(x, df), alpha=0.6, label='chi2 pdf')
plt.title(u'自由度為20時的卡方概率密度函數(shù)圖', fontproperties=titleZW_font_set, size=10)
# 計算平均數(shù)、方差、標(biāo)準(zhǔn)差
# print(chi2.mean(df))
# print(chi2.var(df))
# print(chi2.std(df))
# example ---------------------------------------------------- 標(biāo)準(zhǔn)正態(tài)分布(左側(cè)單邊)
plt.subplot2grid((2, 2), (0, 1))
# print(norm.ppf(0.6179)) # 知道q時求x, q=a
# print(norm.cdf(0.3)) # 知道x時求q
x = np.linspace(norm.ppf(0.01), norm.ppf(0.99), 100)
plt.plot(x, norm.pdf(x), alpha=0.6, label='norm pdf')
plt.title(u'標(biāo)準(zhǔn)正態(tài)分布概率密度函數(shù)圖', fontproperties=titleZW_font_set, size=10)
# example ----------------------------------------------------- t分布(雙邊分布)
plt.subplot2grid((2, 2), (1, 0))
df = 15
x = np.linspace(t.ppf(0.01, df), t.ppf(0.99, df), 100)
# print(t.ppf(0.95, df)) # q=0.95,a=(1-q)*2
# print(t.cdf(1.753, df))
plt.plot(x, t.pdf(x, df), alpha=0.6, label='t pdf')
plt.title(u'自由度為15時的t分布概率密度函數(shù)圖', fontproperties=titleZW_font_set, size=10)
# example ------------------------------------------------------ F分布(右側(cè)單邊分布)
plt.subplot2grid((2, 2), (1, 1))
df = 5
dn = 8
x = np.linspace(f.ppf(0.01, df, dn), f.ppf(0.99, df, dn), 100)
# print(f.ppf(0.95, df, dn))
plt.plot(x, f.pdf(x, df, dn), alpha=0.6, label='f pdf')
plt.title(u'自由度為5和8時的f分布概率密度函數(shù)圖', fontproperties=titleZW_font_set, size=10)
# example ------------------------------------------------------- 非標(biāo)準(zhǔn)正態(tài)分布
plt.figure()
std = 1
mean = 2
normalDistribution = stats.norm(mean, std) # 構(gòu)建統(tǒng)計分布
x = np.linspace(normalDistribution.ppf(0.01), normalDistribution.ppf(0.99), 100)
plt.plot(x, normalDistribution.pdf(x))
# plt.show()
# example -------------------------------------------------------- 對連續(xù)數(shù)據(jù)進(jìn)行正態(tài)擬合
plt.figure()
train = pd.read_csv("csv/Titanic/train.csv")
train_Age = train.dropna(subset=['Age'])
M_S = stats.norm.fit(train_Age['Age']) # 正態(tài)擬合的平均值與標(biāo)準(zhǔn)差
train_Age['Age'].plot(kind='kde') # 原本的概率密度分布圖
normalDistribution = stats.norm(M_S[0], M_S[1]) # 繪制擬合的正態(tài)分布圖
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('Titanic[Age] on NormalDistribution', size=20)
plt.legend(['Origin', 'NormDistribution'])
# ----------------------------------------------------------------- R x C列聯(lián)表，獨(dú)立性檢驗(yàn)
# 建立關(guān)于性別與存活
train_pclass_0 = train['Pclass'][train['Survived'] == 0].value_counts()
train_pclass_1 = train['Pclass'][train['Survived'] == 1].value_counts()
train_pclass_01 = pd.concat([train_pclass_0, train_pclass_1], axis=1, sort=True)
train_pclass_01.columns = ['Not_Survived', 'Survived']
g, p, dof, expctd = chi2_contingency(train_pclass_01.values) # g為chi2值，服從自由度為dof的卡方分布
print(g)
# 擬合優(yōu)度檢驗(yàn)，判斷兩個分類型變量是否獨(dú)立
# 首先繪制卡方自由度為dof的曲線
plt.figure()
x = np.linspace(chi2.ppf(0.01, dof), chi2.ppf(0.99, dof), 100)
plt.plot(x, chi2.pdf(x, dof))
# 以95%置信區(qū)間，查看小概率事件區(qū)間
plt.axvline(chi2.ppf(0.975, dof), color='r')
plt.axvline(chi2.ppf(0.025, dof), color='r')
plt.title('chi2 distribution'+'whose dof is '+str(dof))
plt.text(chi2.ppf(0.975, dof), 0.02, 'q=0.95,z='+str(round(chi2.ppf(0.975, dof), 2)), ha='right', va='top', color='g', alpha=0.8, size=15)
plt.text(chi2.ppf(0.025, dof), 0.02, 'q=0.05,z='+str(round(chi2.ppf(0.025, dof), 2)), ha='left', va='top', color='g', alpha=0.8, size=15)
plt.show()
