x must be of type float, n of type integer.
if np.isnan(n):
return n // Keep the same type of nan
if int(n) != n or n <= 0:
return np.nan
if x >= 1.0 or x <= 0:
return 0
t = n * x
if t <= 1.0:
// Ruben-Gambino: n!/n^n * (2t-1)^n -> 2 n!/n^n * n^2 * (2t-1)^(n-1)
if t <= 0.5:
return 0.0
if n <= 140:
prd = np.prod(np.arange(1, n) * (1.0 / n) * (2 * t - 1))
else:
prd = np.exp(_log_nfactorial_div_n_pow_n(n) + (n-1) * np.log(2 * t - 1))return prd * 2 * n**2
if t >= n - 1:
// Ruben-Gambino : 1-2(1-x)**n -> 2n*(1-x)**(n-1)
return 2 * (1.0 - x) ** (n-1) * n
if x >= 0.5:
return 2 * scipy.stats.ksone.pdf(x, n)
// Just take a small delta.
// Ideally x +/- delta would stay within [i/n, (i+1)/n] for some integer a.
// as the CDF is a piecewise degree n polynomial.
// It has knots at 1/n, 2/n, ... (n-1)/n
// and is not a C-infinity function at the knots
delta = x / 2.0**16
delta = min(delta, x - 1.0/n)
delta = min(delta, 0.5 - x)
def _kk(_x):
return kolmogn(n, _x)
return scipy.misc.derivative(_kk, x, dx=delta, order=5)
def _kolmogni(n, p, q):
Computes the PPF/ISF of kolmogn.
