def kolmogorov(alpha):
"""
:param alpha: the scale parameter
:return: line about accepting or rejecting a hypothesis
"""
arr = np.random.exponential(scale=1 / alpha, size=n) # sample of size n from an exponential distribution
arr = np.sort(arr) # order statistic
k = np.array(range(1, len(arr) + 1))
D = np.maximum(expon.cdf(x=arr, loc=0, scale=1) - (k - 1) / len(arr),
k / len(arr) - expon.cdf(x=arr, loc=0, scale=1)).max()
if np.sqrt(len(arr)) * D < kolmogi(gamma):
return f'D = {D:0.4f}. \nThe statistical data do NOT CONFLICT with the H0 hypothesis.\n'
else:
return f'D = {D:0.4f}. \nThe statistical data do CONFLICT with the H0 hypothesis.\n'
def smirnov(alpha):
"""
Compute the Kolmogorov-Smirnov statistic on 2 samples.
:param alpha: the scale parameter
:return: line about accepting or rejecting a hypothesis
"""
sample_1 = np.sort(np.random.exponential(scale=1, size=n))
sample_2 = np.sort(np.random.exponential(scale=1 / alpha, size=int(n / 2)))
k = np.array(range(1, len(sample_2) + 1))
D = np.maximum(expon.cdf(x=sample_2, loc=0, scale=1) - (k - 1) / len(sample_2),
k / len(sample_2) - expon.cdf(x=sample_2, loc=0, scale=1)).max()
criteria = kolmogi(gamma) * np.sqrt((1 / n) + (1 / (n / 2)))
if D < criteria:
return f'D = {D:0.4f}, criteria = {criteria:0.4f}. \n' \
f'The statistical data do NOT CONFLICT with the H0 hypothesis.'
else:
return f'D = {D:0.4f}, criteria = {criteria:0.4f}. \n' \
f'The statistical data do CONFLICT with the H0 hypothesis.'
def _k_ki(_p):
return kolmogorov(kolmogi(_p))
def test_nan(self):
assert_(np.isnan(kolmogi(np.nan)))
def _ki_k(_x):
return kolmogi(kolmogorov(_x))
def _k_ki(_p):
return kolmogorov(kolmogi(_p))
def test_nan(self):
assert_(np.isnan(kolmogi(np.nan)))
def _ki_k(_x):
return kolmogi(kolmogorov(_x))
from scipy.special import kolmogi
alpha = [0.1, 0.05, 0.025, 0.01]
lmb = kolmogi(alpha)
res = '\\begin{tabular}{|c|c|c|c|c|}\n \\hline \n$\\alpha$ & '
for a in alpha[:-1]:
res += f'{a} & '
res += f'{alpha[-1]} \\\\\n \\hline \n'
res += '$\\lambda_{\\alpha}$ & '
for l in lmb[:-1]:
res += f'{l:.3f} & '
res += f'{lmb[-1]:.3f} \\\\\n \\hline \n'
res += "\\end{tabular}"
with open(".\\tables\\kolmogorov_table_raw.tex", "w") as fin:
fin.write(res)
