python参数估计实战

介绍

本次实战仅仅以总体均值的区间估计做为例子

代码

在这里插入代码import pandas as pd
import numpy as np
from scipy import stats
import math
import seaborn as sns
from matplotlib import pyplot as plt


plt.rcParams['font.sans-serif'] = 'SimHei'
plt.rcParams['axes.unicode_minus'] = False

height = np.arange(160,185,0.01)
height = pd.DataFrame({'height':height})
print(height.describe())
overall_std = (height.std())['height']
overall_mean = (height.mean())['height']

计算正态分布下的置信区间

#方差未知 使用样本方差
def norm_conf1 (data,confidence=0.95):
    sample_mean = np.mean(data)
    sample_std = np.std(data,ddof=1)
    sample_size = len(data)
    conf_intveral = stats.norm.interval(confidence, loc=sample_mean, scale=sample_std)
    print(conf_intveral)

#方差已知 Overall_std
def norm_conf2 (data,std_n,confidence=0.95):
    sample_mean = np.mean(data)
    sample_size = len(data)
    conf_intveral = stats.norm.interval(confidence, loc=sample_mean, scale=std_n)
    print(conf_intveral)

计算T分布下的置信区间

#总体方差未知
def ttest_conf1 (data,confidence=0.95):
    sample_mean = np.mean(data)
    sample_std = np.std(data,ddof=1)
    sample_size = len(data)
    conf_intveral = stats.t.interval(confidence,df = (sample_size-1) , loc=sample_mean, scale=sample_std)
    print(conf_intveral)

#总体方差已知
def ttest_conf2 (data,std_n,confidence=0.95):
    sample_mean = np.mean(data)
    sample_std = np.std(data,ddof=1)
    sample_size = len(data)
    conf_intveral = stats.t.interval(confidence,df = (sample_size-1) , loc=sample_mean, scale=std_n)
    print(conf_intveral)

模拟大样本，非正态分布，总体方差已知和未知的情况

scale_means1 = []
n=100
for _ in range(1000):
   scale_sample1 = height.sample(n, replace=True)
   mean1 = scale_sample1.mean()
   scale_means1.append(mean1)
sns.set_palette("hls") #设置所有图的颜色，使用hls色彩空间
sns.distplot(scale_means1,color="r",bins=10,kde=True)
plt.title('Height')
plt.xlim(165,180)
plt.grid(True)
plt.show()   
# 总体非正态样本 方差未知
print('---------非正态，方差未知，大样本---------------------')
norm_conf1(scale_means1)
print('---------非正态，方差已知，大样本---------------------')
# 总体非正太样本 方差已知
norm_conf2(scale_means1,overall_std/math.sqrt(n))

模拟正态分布总体，大小样本，总体方差已知和未知情况

# 总体正态分布 是用上面数据的均值和方差进行正态分布模拟
normalHeight = np.random.normal(overall_mean, overall_std,2500)
normalHeight = pd.DataFrame({'normalHeight':normalHeight})

scale_means2 = []
n=20
for _ in range(1000):
   scale_sample2 = normalHeight.sample(n, replace=True)
   mean2 = scale_sample2.mean()
   scale_means2.append(mean2)
sns.set_palette("hls") #设置所有图的颜色，使用hls色彩空间
sns.distplot(scale_means2,color="r",bins=10,kde=True)
plt.title('Height')
plt.xlim(165,180)
plt.grid(True)
plt.show()   
#小样本使用t分布
print('---------正态，方差为未知，小样本---------------------')
ttest_conf1(scale_means2)
print('---------正态，方差为已知，小样本---------------------')
ttest_conf2(scale_means2,overall_std/math.sqrt(n))

scale_means2 = []
n=100
for _ in range(1000):
   scale_sample2 = normalHeight.sample(n, replace=True)
   mean2 = scale_sample2.mean()
   scale_means2.append(mean2)

print('---------正态，方差为未知，大样本---------------------')
norm_conf1(scale_means2)
print('---------正态，方差为已知，大样本---------------------')
norm_conf2(scale_means2,overall_std/math.sqrt(n))