def test_erfinv_extreme_values():
x_near_n1 = np.nextafter(-1, np.inf)
assert_allclose(
sc.erfinv(x_near_n1),
float(mpmath.erfinv(x_near_n1)),
atol=0,
rtol=1e-14,
)
x_near_1 = np.nextafter(1, -np.inf)
assert_allclose(
sc.erfinv(x_near_1),
float(mpmath.erfinv(x_near_1)),
atol=0,
rtol=1e-14,
)
def _invert_Gaussian_CDF(self, z):
if z < 0.5:
sign = -1
else:
sign = 1
x = sign*np.sqrt(2)*mpmath.erfinv(sign*(2*z-1))
return(float(x))
def t2z_convert(t, nu):
t = mpf(t)
nu = mpf(nu)
z = sqrt(mpf("2")) * erfinv( # inverse normal cdf
mpf("2") * t *
gamma((mpf("1") / mpf("2")) * nu + mpf("1") / mpf("2")) * hyper(
(mpf("1") / mpf("2"),
(mpf("1") / mpf("2")) * nu + mpf("1") / mpf("2")),
(mpf("3") / mpf("2"), ),
-power(t, mpf("2")) / nu,
) / (sqrt(pi) * sqrt(nu) * gamma((mpf("1") / mpf("2")) * nu)))
return z
def invsf(p, mu=0, sigma=1):
"""
Inverse of the survivial function of the Lévy distribution.
"""
if p < 0 or p > 1:
raise ValueError('p must be in the interval [0, 1]')
if sigma <= 0:
raise ValueError('sigma must be positive.')
with mpmath.extradps(5):
p = mpmath.mpf(p)
mu = mpmath.mpf(mu)
sigma = mpmath.mpf(sigma)
return mu + sigma / (2 * mpmath.erfinv(p)**2)
def f2z_convert(x, d1, d2):
x = mpf(x)
d1 = mpf(d1)
d2 = mpf(d2)
if x < mpf("0") or d1 < mpf("0") or d2 < mpf("0"):
return mpf("0")
z = sqrt(mpf("2")) * erfinv( # inverse normal cdf
-mpf("1") + mpf("2") * betainc( # F distribution cdf
d1 / mpf("2"),
d2 / mpf("2"),
x2=d1 * x / (d1 * x + d2),
regularized=True))
return z
def ZPL_bayesiana(Non, Noff, vol):
alpha = (1 - vol) / (vol)
def B_01(Non, Noff, alpha):
Ntot = Non + Noff
gam = (1 + 2 * Noff) * power(alpha, (0.5 + Ntot)) * gamma(0.5 + Ntot)
delta = ((2 * power((1 + alpha), Ntot)) * gamma(1 + Ntot) *
hyp2f1(0.5 + Noff, 1 + Ntot, 1.5 + Noff, (-1 / alpha)))
c1_c2 = sqrt(pi) / (2 * atan(1 / sqrt(alpha)))
return gam / (c1_c2 * delta)
buf = 1 - B_01(Non, Noff, alpha)
if buf < -1.0:
buf = -1.0
# print(buf)
return sqrt("2") * erfinv(buf)
def invcdf(p, mu=0, sigma=1):
"""
Normal distribution inverse CDF.
This function is also known as the quantile function or the percent
point function.
"""
if p < 0 or p > 1:
return mpmath.nan
p = mpmath.mpf(p)
mu = mpmath.mpf(mu)
sigma = mpmath.mpf(sigma)
a = mpmath.erfinv(2 * p - 1)
x = mpmath.sqrt(2) * sigma * a + mu
return x
def invcdf(p, mu=0, sigma=1):
"""
Log-normal distribution inverse CDF.
This function is also known as the quantile function or the percent
point function.
"""
_validate_sigma(sigma)
if p < 0 or p > 1:
return mpmath.nan
with mpmath.extradps(5):
p = mpmath.mpf(p)
mu = mpmath.mpf(mu)
sigma = mpmath.mpf(sigma)
a = mpmath.erfinv(2 * p - 1)
x = mpmath.exp(mpmath.sqrt(2) * sigma * a + mu)
return x
def _comp_beta(self, eps_exp):
eps = mpm.power(2, eps_exp)
beta = mpm.erfinv(1 - eps) * mpm.sqrt(2)
return beta
def mpmath_erfcinv(x):
return mpmath.erfinv(mpmath.mpf(1) - x)
def pvalue2sigma(self, pvalue):
return mpmath.sqrt(2) * mpmath.erfinv(1 - 2 * pvalue)
def inverseNormalCDF(area):
return mpmath.erfinv(area) * mpmath.sqrt(2.0)
def _erfcinv(y):
with mpmath.extradps(5):
return mpmath.erfinv(1 - y)