def _kolmogni(n, p, q):
"""Computes the PPF/ISF of kolmogn.
n of type integer, n>= 1
p is the CDF, q the SF, p+q=1
"""
if np.isnan(n):
return n # Keep the same type of nan
if int(n) != n or n <= 0:
return np.nan
if p <= 0:
return 1.0 / n
if q <= 0:
return 1.0
delta = np.exp((np.log(p) - scipy.special.loggamma(n + 1)) / n)
if delta <= 1.0 / n:
return (delta + 1.0 / n) / 2
x = -np.expm1(np.log(q / 2.0) / n)
if x >= 1 - 1.0 / n:
return x
x1 = scu._kolmogci(p) / np.sqrt(n)
x1 = min(x1, 1.0 - 1.0 / n)
_f = lambda x: _kolmogn(n, x) - p
return scipy.optimize.brentq(_f, 1.0 / n, x1, xtol=1e-14)
def _kci_kc(_x):
return _kolmogci(_kolmogc(_x))
def _kci_kc(_x):
return _kolmogci(_kolmogc(_x))