python3 概率论作业2

from scipy.stats import *

# 标准正太分布
x = norm()
print(
x.mean(), x.var(), x.std()
)

# 构造置信区间，验证置信度

rvs_size = 10000
degrees = [
0.01,
0.05,
0.1,
]

test_size = 10000

for degree in degrees:
cnt = 0
# 置信度应该是1-degree
for i in range(test_size):
rvs = x.rvs(size=rvs_size)

m = rvs.mean()
a = (m - 1 / rvs_size ** 0.5 * x.isf(degree / 2))
b = (m + 1 / rvs_size ** 0.5 * x.isf(degree / 2))

# 置信区间为[a, b]
if a <= 0 <= b:
# 均值在置信区间内，标记加一
cnt += 1

print(
'degree={0}'.format(degree),
'理论值：{0}'.format(1 - degree),
'统计值：{0}'.format(cnt / test_size)
)

0.0 1.0 1.0
degree=0.01 理论值：0.99 统计值：0.9903
degree=0.05 理论值：0.95 统计值：0.9543
degree=0.1 理论值：0.9 统计值：0.9064