Python's random
module has the following method in it:
def gammavariate(self, alpha, beta):
"""Gamma distribution. Not the gamma function!
Conditions on the parameters are alpha > 0 and beta > 0.
The probability distribution function is:
x ** (alpha - 1) * math.exp(-x / beta)
pdf(x) = --------------------------------------
math.gamma(alpha) * beta ** alpha
"""
# alpha > 0, beta > 0, mean is alpha*beta, variance is alpha*beta**2
# Warning: a few older sources define the gamma distribution in terms
# of alpha > -1.0
if alpha <= 0.0 or beta <= 0.0:
raise ValueError('gammavariate: alpha and beta must be > 0.0')
random = self.random
if alpha > 1.0:
# Uses R.C.H. Cheng, "The generation of Gamma
# variables with non-integral shape parameters",
# Applied Statistics, (1977), 26, No. 1, p71-74
ainv = _sqrt(2.0 * alpha - 1.0)
bbb = alpha - LOG4
ccc = alpha + ainv
while 1:
u1 = random()
if not 1e-7 < u1 < .9999999:
continue
u2 = 1.0 - random()
v = _log(u1/(1.0-u1))/ainv
x = alpha*_exp(v)
z = u1*u1*u2
r = bbb+ccc*v-x
if r + SG_MAGICCONST - 4.5*z >= 0.0 or r >= _log(z):
return x * beta
elif alpha == 1.0:
# expovariate(1)
u = random()
while u <= 1e-7:
u = random()
return -_log(u) * beta
else: # alpha is between 0 and 1 (exclusive)
# Uses ALGORITHM GS of Statistical Computing - Kennedy & Gentle
while 1:
u = random()
b = (_e + alpha)/_e
p = b*u
if p <= 1.0:
x = p ** (1.0/alpha)
else:
x = -_log((b-p)/alpha)
u1 = random()
if p > 1.0:
if u1 <= x ** (alpha - 1.0):
break
elif u1 <= _exp(-x):
break
return x * beta
While porting the code over to Java for use, my IDE has been complaining that there is a typo (misspelling) for the ainv
variable name. Where does this name come from, and what is the justification behind it? If anyone can find reference material for Applied Statistics, (1977), 26, No. 1, p71-74, being able to read those pages may be helpful.
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