python - python scipy.stats 中的 norm.ppf 与 norm.cdf

Question

所以我已经粘贴了我的完整代码供您引用，我想知道这里的ppf和cdf有什么用？你能解释一下吗？我做了一些研究，发现 ppf(百分比点函数)是 CDF(累积分布函数)的倒数
如果确实如此，如果我将 ppf 和 cdf 分别替换为 1/cdf 和 1/ppf，这段代码不应该工作吗？
请向我解释这一点，两者之间的区别。以及如何以及何时使用哪个
这是，顺便说一句，假设检验。
很抱歉有这么多评论，只是为了我以后的引用而解释一切的习惯。(如果我的评论有任何错误，请指出我)

ball_bearing_radius = [2.99, 2.99, 2.70, 2.92, 2.88, 2.92, 2.82, 2.83, 3.06, 2.85]




import numpy as np

from math import sqrt
from scipy.stats import norm

# h1 : u != U_0
# h0 : u = u_0
#case study : ball bearing example, claim is that radius = 3, do hypothesis testing 
mu_0 = 3
sigma = 0.1

#collect sample
sample = ball_bearing_radius

#compute mean
mean = np.mean(sample)

#compute n
n = len(sample)

#compute test statistic
z = (mean - mu_0) /(sigma/sqrt(n))

#set alpha
a = 0.01

#-------------------------

#calculate the z_a/2, by using percent point function of the norm of scipy
#ppf = percent point function, inverse of CDF(comulative distribution function)
#also, CDF = pr(X<=x), i.e., probability to the left of the distribution

z_critical = norm.ppf(1-a/2)    #this returns a value for which the probab to the left is 0.975

p_value = 2*(1 - norm.cdf(np.abs(z)))

p_value = float("{:.4f}".format(p_value))


print('z : ',z)
print('\nz_critical :', z_critical)
print('\nmean :', mean, "\n\n")

#test the hypothesis

if (np.abs(z) > z_critical):
    print("\nREJECT THE NULL HYPOTHESIS : \n p-value = ", p_value, "\n Alpha = ", a )

else:
    print("CANNOT REJECT THE NULL HYPOTHESIS. NOT ENOUGH EVIDENCE TO REJECT IT: \n p-value = ", p_value, "\n Alpha = ", a )

Answer 1

.ppf() 函数计算给定正态分布值的概率，而 .cdf() 函数计算给定概率是所需值的正态分布值。在这个特殊的意义上，它们是互逆的。
为了说明这个计算，检查下面的示例代码。

from scipy.stats import norm
print(norm.ppf(0.95))
print(norm.cdf(1.6448536269514722))

带有上面代码的这张图片应该让你一目了然。
谢谢!