def rwiener(self, tau, xmin=float('-inf'), xmax=float('inf'), \
pmin=0.0, pmax=1.0):
"""
Generates random numbers corrsponding to a Wiener process (the
intergral of white noise (Langevin's function)), inverse variant.
The Wiener process is W(t+tau) - W (t) = N(0, sqrt(tau))
where tau is the time increment and N(0, sqrt(tau)) is a
normally distributed random variable having zero mean and
sqrt(tau) as its standard deviation.
This method returns W(t+tau) - W(t) given tau and allows
tau to be negative.
"""
self._checkminmax(xmin, xmax, pmin, pmax, 'rwiener')
mu = 0.0
sigma = sqrt(abs(tau)) # abs(tau) is used
pmn = pmin
pmx = pmax
if xmin > float('-inf'): pmn = max(pmin, cnormal(mu, sigma, xmin))
if xmax < float('inf'): pmx = min(pmax, cnormal(mu, sigma, xmax))
p = pmn + (pmx-pmn)*self.runif01()
w = inormal(p, mu, sigma)
return w
def normalscores(ivector, scheme="van_der_Waerden", bottominteger=0):
"""
Creates a list of Blom, Tukey or van der Waerden normal scores given a list
of N integers in [0, N) or [1, N] depending on whether the bottom integer
for the ranking is set to 0 or 1 (0 is default). scheme is either 'Blom',
'Tukey' or 'van_der_Waerden'.
"""
assert bottominteger == 0 or bottominteger == 1, \
"Bottom rank must be set to 0 or 1 in normalscores!"
if scheme == 'Blom':
constnumer = - 0.375
constdenom = 0.250
elif scheme == 'Tukey':
constnumer = - 1.0/3.0
constdenom = - constnumer
elif scheme == 'van_der_Waerden':
constnumer = 0.0
constdenom = 1.0
length = len(ivector)
scorevector = []
for integer in ivector:
n = integer + 1 - bottominteger
scorevector.append(inormal((n-constnumer)/(length+constdenom)))
return scorevector
def normalscores(ivector, scheme="van_der_Waerden", bottominteger=0):
"""
Creates a list of Blom, Tukey or van der Waerden normal scores given a list
of N integers in [0, N) or [1, N] depending on whether the bottom integer
for the ranking is set to 0 or 1 (0 is default). scheme is either 'Blom',
'Tukey' or 'van_der_Waerden'.
"""
assert bottominteger == 0 or bottominteger == 1, \
"Bottom rank must be set to 0 or 1 in normalscores!"
if scheme == 'Blom':
constnumer = -0.375
constdenom = 0.250
elif scheme == 'Tukey':
constnumer = -1.0 / 3.0
constdenom = -constnumer
elif scheme == 'van_der_Waerden':
constnumer = 0.0
constdenom = 1.0
length = len(ivector)
scorevector = []
for integer in ivector:
n = integer + 1 - bottominteger
scorevector.append(inormal((n - constnumer) / (length + constdenom)))
return scorevector
def rnormal(self, mu, sigma, xmin=float('-inf'), xmax=float('inf'), \
pmin=0.0, pmax=1.0):
"""
Generator of normally distributed random variates using an inverse
method, claimed to give a maximum relative error less than 2.6e-9
(cf. statlib.invcdf.inormal for details).
"""
self._checkminmax(xmin, xmax, pmin, pmax, 'rnormal')
pmn = pmin
pmx = pmax
if xmin > float('-inf'): pmn = max(pmin, cnormal(mu, sigma, xmin))
if xmax < float('inf'): pmx = min(pmax, cnormal(mu, sigma, xmax))
p = pmn + (pmx-pmn)*self.runif01()
x = inormal(p, mu, sigma)
return x
def _studQ(ndf, confdeg=0.90):
"""
Quantiles for Student's "t" distribution (one number is returned)
---------
ndf the number of degrees of freedom
confdeg confidence level
--------
Accuracy in decimal digits of about:
5 if ndf >= 8., machine precision if ndf = 1. or 2., 3 otherwise
----------
Reference: G.W. Hill, Communications of the ACM, Vol. 13, no. 10, Oct. 1970
"""
# Error handling
assert 0.0 <= confdeg and confdeg <= 1.0, \
"Confidence degree must be in [0.0, 1.0] in _studQ!"
assert ndf > 0.0, "Number of degrees of freedom must be positive in _studQ!"
phi = 1.0 - confdeg
# For ndf = 1 we can use the Cauchy distribution
if ndf == 1.0:
prob = 1.0 - 0.5*phi
stud = icauchy(prob)
# Finns exakt metod aven for ndf = 2
elif ndf == 2.0:
if phi <= TINY: phi = TINY
stud = sqrt(2.0 / (phi*(2.0-phi)) - 2.0)
# Check to see if we're not too far out in the tails
elif phi < TINY:
t = 1.0 / TINY
stud = t
# General case
else:
a = 1.0 / (ndf-0.5)
b = 48.0 / a**2
c = ((20700.0*a/b - 98.0) * a - 16.0) * a + 96.36
d = ((94.5/(b + c) - 3.0) / b + 1.0) * sqrt(a*PIHALF) * ndf
x = d * phi
y = x ** (2.0 / ndf)
if y > 0.05 + a: # Asymptotic inverse expansion about normal
x = inormal(0.5*phi)
y = x**2
if ndf < 5.0: c = c + 0.3 * (ndf-4.5) * (x+0.6)
c = (((0.05 * d * x - 5.0) * x - 7.0) * x - 2.0) * x + b + c
y = (((((0.4*y + 6.3) * y + 36.0) * y + 94.5) / c - y - 3.0) \
/ b + 1.0) * x
y = a * y**2
if y > 0.002: y = exp(y) - 1.0
else: y = 0.5 * y**2 + y
else:
y = ((1.0 / (((ndf + 6.0) / (ndf * y) - 0.089 * d - \
0.822) * (ndf + 2.0) * 30) + 0.5 / (ndf + 4.0)) \
* y - 1.0) * (ndf + 1.0) / (ndf + 2.0) + 1.0 / y
stud = sqrt(ndf*y)
return stud
def _studQ(ndf, confdeg=0.90):
"""
Quantiles for Student's "t" distribution (one number is returned)
---------
ndf the number of degrees of freedom
confdeg confidence level
--------
Accuracy in decimal digits of about:
5 if ndf >= 8., machine precision if ndf = 1. or 2., 3 otherwise
----------
Reference: G.W. Hill, Communications of the ACM, Vol. 13, no. 10, Oct. 1970
"""
# Error handling
assert 0.0 <= confdeg and confdeg <= 1.0, \
"Confidence degree must be in [0.0, 1.0] in _studQ!"
assert ndf > 0.0, "Number of degrees of freedom must be positive in _studQ!"
phi = 1.0 - confdeg
# For ndf = 1 we can use the Cauchy distribution
if ndf == 1.0:
prob = 1.0 - 0.5 * phi
stud = icauchy(prob)
# Finns exakt metod aven for ndf = 2
elif ndf == 2.0:
if phi <= TINY: phi = TINY
stud = sqrt(2.0 / (phi * (2.0 - phi)) - 2.0)
# Check to see if we're not too far out in the tails
elif phi < TINY:
t = 1.0 / TINY
stud = t
# General case
else:
a = 1.0 / (ndf - 0.5)
b = 48.0 / a**2
c = ((20700.0 * a / b - 98.0) * a - 16.0) * a + 96.36
d = ((94.5 / (b + c) - 3.0) / b + 1.0) * sqrt(a * PIHALF) * ndf
x = d * phi
y = x**(2.0 / ndf)
if y > 0.05 + a: # Asymptotic inverse expansion about normal
x = inormal(0.5 * phi)
y = x**2
if ndf < 5.0: c = c + 0.3 * (ndf - 4.5) * (x + 0.6)
c = (((0.05 * d * x - 5.0) * x - 7.0) * x - 2.0) * x + b + c
y = (((((0.4*y + 6.3) * y + 36.0) * y + 94.5) / c - y - 3.0) \
/ b + 1.0) * x
y = a * y**2
if y > 0.002: y = exp(y) - 1.0
else: y = 0.5 * y**2 + y
else:
y = ((1.0 / (((ndf + 6.0) / (ndf * y) - 0.089 * d - \
0.822) * (ndf + 2.0) * 30) + 0.5 / (ndf + 4.0)) \
* y - 1.0) * (ndf + 1.0) / (ndf + 2.0) + 1.0 / y
stud = sqrt(ndf * y)
return stud