def clevy(scale, x):
"""
The cdf of the Levy distribution (stable distribution with
alpha = 1/2 and beta = 1, aka the Cournot distribution).
This is actually the right-skewed Levy!
f = sqrt(s/2pi) * (1/x)**(3/2) * exp(-s/2x)
F = erfc(sqrt(s/2x))
s >= 0.0, x >= 0
"""
assert scale >= 0.0, "scale must not be negative in clevy!"
assert x >= 0.0, "variate must not be negative in clevy!"
# The cdf of the Levy can be handled since it is an "incomplete gamma
# function", but it seems to be more simple than that:
try:
cdf = erfc1(sqrt(0.5 * scale / x))
except (OverflowError, ZeroDivisionError):
return 0.0
cdf = kept_within(0.0, cdf, 1.0)
return cdf
def clevy(scale, x):
"""
The cdf of the Levy distribution (stable distribution with
alpha = 1/2 and beta = 1, aka the Cournot distribution).
This is actually the right-skewed Levy!
f = sqrt(s/2pi) * (1/x)**(3/2) * exp(-s/2x)
F = erfc(sqrt(s/2x))
s >= 0.0, x >= 0
"""
assert scale >= 0.0, "scale must not be negative in clevy!"
assert x >= 0.0, "variate must not be negative in clevy!"
# The cdf of the Levy can be handled since it is an "incomplete gamma
# function", but it seems to be more simple than that:
try:
cdf = erfc1(sqrt(0.5 * scale / x))
except (OverflowError, ZeroDivisionError):
return 0.0
cdf = kept_within(0.0, cdf, 1.0)
return cdf
# end of clevy
# ------------------------------------------------------------------------------
def cnormal(mu, sigma, x):
"""
cdf for the normal (Gaussian) distribution based on the erfc1 function
that offers an estimated maximum fractional error < 50*machine epsilon.
sigma > 0.0
"""
assert sigma > 0.0, "sigma must be a positive float in cnormal!"
x = (x - mu) / float(sigma)
y = SQRT05 * abs(x)
cdf = 0.5 * erfc1(y)
if x > 0.0: cdf = 1.0 - cdf
cdf = kept_within(0.0, cdf, 1.0)
return cdf
def cnormal(mu, sigma, x):
"""
cdf for the normal (Gaussian) distribution based on the erfc1 function
that offers an estimated maximum fractional error < 50*machine epsilon.
sigma > 0.0
"""
assert sigma > 0.0, "sigma must be a positive float in cnormal!"
x = (x - mu) / float(sigma)
y = SQRT05 * abs(x)
cdf = 0.5 * erfc1(y)
if x > 0.0:
cdf = 1.0 - cdf
cdf = kept_within(0.0, cdf, 1.0)
return cdf