#!/usr/bin/env python
# coding: utf-8

# # p-values from n-sigma and vice versa

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import scipy.stats as st


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# define p-value
p = 0.0456


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# calculate number of standard deviations (n-sigma) from p-value

# one-tailed
n_sigma_one_tailed = st.norm.ppf(1-p)

# two-tailed
n_sigma_two_tailed = st.norm.ppf(1-p/2.)

print(f" p-value = {p}, n_sigma_one_tailed = {n_sigma_one_tailed:.4f}, n_sigma_two_tailed = {n_sigma_two_tailed:.4f}")


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# p-value from number of standard deviations (n-sigma)
n_sigma = 5

# one-tailed
p_value_one_tailed = 1 - st.norm.cdf(n_sigma)

# two-tailed
p_value_two_tailed = 2. * (1 - st.norm.cdf(n_sigma))

print(f" n-sigma = {n_sigma}, p_value_one_tailed = {p_value_one_tailed:.2g}, p_value_two_tailed = {p_value_two_tailed:.2g}")


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for nsigma in [1, 2, 3, 4, 5]:
    p_value_one_tailed = 1 - st.norm.cdf(nsigma)
    print(f"{nsigma} {p_value_one_tailed:.2g}")


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