def f_test(data1, data2, tail="both", ratio=1):
"""
F 分布
:param data1: 样本值 1
:param data2: 样本值 2
:param tail: 尾类型
:param ratio:
:return:
"""
assert tail in ["both", "left", "right"], \
'tail should be one of “both”, “left”, “right”'
n1 = len(data1)
n2 = len(data2)
sample1_var = variance(data1)
sample2_var = variance(data2)
f_val = sample1_var / sample2_var / ratio
df1 = n1 - 1
df2 = n2 - 1
if tail == "both":
p = 2 * min(1 - f.cdf(f_val, df1, df2), f.cdf(f_val, df1, df2))
elif tail == "left":
p = f.cdf(f_val, df1, df2)
else:
p = 1 - f.cdf(f_val, df1, df2)
return f_val, df1, df2, p
def mean_diff_ci_t_est(data1, data2, alpha, equal=True):
# 样本容量 1
n1 = len(data1)
# 样本容量 2
n2 = len(data2)
# 均值差
mean_diff = mean(data1) - mean(data2)
# 样本方差
sample1_var = variance(data1)
sample2_var = variance(data2)
# 两个总体方差未知且相等，求均值差的置信区间
if equal:
# 联合标准差
sw = sqrt(
((n1 - 1) * sample1_var + (n2 - 1) * sample2_var) / (n1 + n2 - 2))
t_value = abs(t.ppf(alpha / 2, n1 + n2 - 2))
return mean_diff - sw * sqrt(1 / n1 + 1 / n2) * t_value, \
mean_diff + sw * sqrt(1 / n1 + 1 / n2) * t_value
# 两个总体方差未知且不等，求均值差的置信区间
else:
# 自由度
# 分子
df_numerator = (sample1_var / n1 + sample2_var / n2)**2
# 分母
df_denominator = (sample1_var / n1)**2 / (n1 - 1) + (sample2_var /
n2)**2 / (n2 - 1)
df = df_numerator / df_denominator
t_value = abs(t.ppf(alpha / 2, df))
return mean_diff - sqrt(sample1_var / n1 + sample2_var / n2) * t_value, \
mean_diff + sqrt(sample1_var / n1 + sample2_var / n2) * t_value
def var_ratio_ci_est(data1, data2, alpha):
# 样本容量 1
n1 = len(data1)
# 样本容量 2
n2 = len(data2)
# 置信下限
f_lower_value = f.ppf(alpha / 2, n1 - 1, n2 - 1)
# 置信上限
f_upper_value = f.ppf(1 - alpha / 2, n1 - 1, n2 - 1)
# 方差比
var_ratio = variance(data1) / variance(data2)
return var_ratio / f_upper_value, var_ratio / f_lower_value
def t_test(data1, data2=None, tail="both", mu=0, equal=True):
"""
t检验
:param data1: 样本 1
:param data2: 样本 2
:param tail: 是否双尾检验， 默认是
:param mu: μ值
:param equal:
:return:
"""
assert tail in ["both", "left", "right"], \
'tail should be one of "both", "left", "right"'
if data2 is None:
mean_val = mean(data1)
se = std(data1) / sqrt(len(data1))
t_val = (mean_val - mu) / se
df = len(data1) - 1
else:
n1 = len(data1)
n2 = len(data2)
mean_diff = mean(data1) - mean(data2)
sample1_var = variance(data1)
sample2_var = variance(data2)
if equal:
sw = sqrt(((n1 - 1) * sample1_var + (n2 - 1) * sample2_var) /
(n1 + n2 - 2))
t_val = (mean_diff - mu) / (sw * sqrt(1 / n1 + 1 / n2))
df = n1 + n2 - 2
else:
se = sqrt(sample1_var / n1 + sample2_var / n2)
t_val = (mean_diff - mu) / se
df_numerator = (sample1_var / n1 + sample2_var / n2)**2
df_denominator = (sample1_var / n1)**2 / (n1 - 1) + (
sample2_var / n2)**2 / (n2 - 1)
df = df_numerator / df_denominator
if tail == "both":
p = 2 * (1 - t.cdf(abs(t_val), df))
elif tail == "left":
p = t.cdf(t_val, df)
else:
p = 1 - t.cdf(t_val, df)
return t_val, df, p
def var_ci_est(data, alpha):
"""方差的置信区间"""
n = len(data)
s2 = variance(data)
# 卡方分布
chi2_lower_value = chi2.ppf(alpha / 2, n - 1)
chi2_upper_value = chi2.ppf(1 - alpha / 2, n - 1)
return (n - 1) * s2 / chi2_upper_value, (n - 1) * s2 / chi2_lower_value
def simple_linear_reg(y, x):
"""一元线性回归"""
assert len(x) == len(y)
n = len(x)
assert n > 1
mean_x = mean(x)
mean_y = mean(y)
beta1 = covariance(x, y) / variance(x)
beta0 = mean_y - beta1 * mean_x
y_hat = [beta0 + beta1 * e for e in x]
ss_residual = sum((e1 - e2)**2 for e1, e2 in zip(y, y_hat))
se_model = sqrt(ss_residual / (n - 2))
t_value = beta1 / (se_model / sqrt((n - 1) * variance(x)))
p = 2 * (1 - t.cdf(abs(t_value), n - 2))
return beta0, beta1, t_value, n - 2, p
def chi2_test(data, tail="both", sigma2=1):
"""
卡方分布
:param data: 样本值
:param tail: 尾类型
:param sigma2: μ
:return:
"""
assert tail in ["both", "left", "right"], \
'tail should be one of “both”, “left”, “right”'
n = len(data)
sample_var = variance(data)
chi2_val = (n - 1) * sample_var / sigma2
if tail == "both":
p = 2 * min(1 - chi2.cdf(chi2_val, n - 1), chi2.cdf(chi2_val, n - 1))
elif tail == "left":
p = chi2.cdf(chi2_val, n - 1)
else:
p = 1 - chi2.cdf(chi2_val, n - 1)
return chi2_val, n - 1, p
zws2 = median(data_zws2)
zws3 = median(data_zws3)
print("zws", zws1, zws2, zws3) # 再次认证中位数和极端值没有关联，是集中趋势
# 测试均值
data_jz = [1, 2, 3, 4, 5]
jz = mean(data_jz)
print("jz", jz)
# 测试极差
data_jc = [1, 2, 3, 999]
jc = rng(data_jc)
print("jc", jc)
# 测试四分位数
data_sfws = [1, 4, 2, 3, 5]
sfws = quartile(data_sfws)
print(sfws)
# 测试方差
data_fc = [1, 4, 2, 3, 5]
fc = variance(data_fc)
bzc = std(data_fc)
print(fc, bzc)
# 测试协方差,相关系数
score = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
happy = [1, 3, 2, 6, 4, 5, 8, 10, 9, 7]
print(covariance(score, happy))
print(cor(score, happy))
import random
import matplotlib.pyplot as plt
from stats.descriptive_stats import mean, variance
if __name__ == '__main__':
"""相合性"""
# 样本均值
sample_means = []
# 样本方差
sample_vars = []
# 样本容量
indices = []
for sz in range(20, 10001, 50):
indices.append(sz)
# 调用高斯分布
sample = [random.gauss(0.0, 1.0) for _ in range(sz)]
sample_means.append(mean(sample))
sample_vars.append(variance(sample))
plt.plot(indices, sample_means)
plt.plot(indices, sample_vars)
"""结论，当样本越大时，样本均值逐渐趋向于样本方差,这就是相合性。"""
plt.show()