def dNexpo(means, x):
"""
The pdf of the distribution of a sum of exponentially distributed
random variables.
NB Means are allowed to be equal (but the function is slow)!!!
"""
assert x >= 0.0, "variate must not be negative in dNexpo!"
number = len(means)
if number == 1: return dexpo(means[0], x)
if x == 0.0:
if number == 1: return 1.0 / means[0]
else: return 0.0
lam = []
for k in range(0, number):
assert means[k] > 0.0, "All means must be positive floats in dNexpo!"
lam.append(1.0 / means[k])
# ----------------------------------------------------
def _ftilde(z):
zprod = complex(1.0)
for k in range(0, number):
zprod = zprod * complex(lam[k]) / (z + lam[k])
return zprod
# ----------------------------------------------------
rpole = -min(lam)
sigma = (1.0 - TWOMACHEPS) * rpole
pdf = talbot(_ftilde, x, sigma)
pdf = kept_within(0.0, pdf)
return pdf
def cNexpo(means, x):
"""
cdf of a distribution of a sum of exponentially distributed
random variables.
NB Means are allowed to be equal (but the function is slow)!!!
"""
assert x >= 0.0, "variate must not be negative in cNexpo!"
if x == 0.0:
return 0.0
number = len(means)
if number == 1:
return cexpo(means[0], x)
lam = []
for k in range(0, number):
assert means[k] > 0.0, "All means must be positive floats in cNexpo!"
lam.append(1.0 / means[k])
# ----------------------------
def ftilde(z):
zprod = complex(1.0)
for k in range(0, number):
zprod = zprod * complex(lam[k]) / (z + lam[k])
zprod = zprod / z
return zprod
# -----------------------------
sigma = TWOMACHEPS * min(lam)
cdf = talbot(ftilde, x, sigma)
cdf = kept_within(0.0, cdf, 1.0)
return cdf
def dNexpo(means, x):
"""
The pdf of the distribution of a sum of exponentially distributed
random variables.
NB Means are allowed to be equal (but the function is slow)!!!
"""
assert x >= 0.0, "variate must not be negative in dNexpo!"
number = len(means)
if number == 1: return dexpo(means[0], x)
if x == 0.0:
if number == 1: return 1.0/means[0]
else: return 0.0
lam = []
for k in range(0, number):
assert means[k] > 0.0, "All means must be positive floats in dNexpo!"
lam.append(1.0/means[k])
# ----------------------------------------------------
def _ftilde(z):
zprod = complex(1.0)
for k in range(0, number):
zprod = zprod * complex(lam[k]) / (z+lam[k])
return zprod
# ----------------------------------------------------
rpole = - min(lam)
sigma = (1.0-TWOMACHEPS) * rpole
pdf = talbot(_ftilde, x, sigma)
pdf = kept_within(0.0, pdf)
return pdf
def cNexpo(means, x):
"""
cdf of a distribution of a sum of exponentially distributed
random variables.
NB Means are allowed to be equal (but the function is slow)!!!
"""
assert x >= 0.0, "variate must not be negative in cNexpo!"
if x == 0.0: return 0.0
number = len(means)
if number == 1: return cexpo(means[0], x)
lam = []
for k in range(0, number):
assert means[k] > 0.0, "All means must be positive floats in cNexpo!"
lam.append(1.0 / means[k])
# ----------------------------
def ftilde(z):
zprod = complex(1.0)
for k in range(0, number):
zprod = zprod * complex(lam[k]) / (z + lam[k])
zprod = zprod / z
return zprod
#-----------------------------
sigma = TWOMACHEPS * min(lam)
cdf = talbot(ftilde, x, sigma)
cdf = kept_within(0.0, cdf, 1.0)
return cdf
