Computer Generation of Gamma Random Variates
with Non-integral Shape Parameters

When the shape parameter, a, is integral,
generating gamma random variables with a digital 
computer is straightforward.  There is no simple method
for generating gamma random variates with non-integral 
shape parameters.  A common procedure is to approximately
generate such random variables by use of the 
so-called probability switch method.  Another procedure,
which is exact, is due to Johnk.  This paper 
presents a rejection method for exactly generating
gamma random variables when a is greater than 1.  
The efficiency of the rejection method is shown to
be better than the efficiency of Johnk's method.  
The paper concludes that when a is non-integral the following
mix of procedures yields the best combination 
of accuracy and efficiency: (1) when a is less than
1, use Johnk's method; (2) when 1 is less than a 
and a is less than 5, use the rejection method; (3) when
a is greater than 5, use the probability switch 
method.

CACM December,1974

Wallace, N. D.

simulation, gamma random variables,
probability distribution, random numbers

5.5 8.1

CA741205 JB January 16, 1978  9:35 AM

2569	5	2569
2569	5	2569
2569	5	2569
2847	5	2569
2928	5	2569
3046	5	2569
3098	5	2569
3107	5	2569
1751	6	2569
2277	6	2569
2380	6	2569
2522	6	2569
2569	6	2569
2569	6	2569
2569	6	2569
2569	6	2569
2569	6	2569
2847	6	2569
2847	6	2569
3098	6	2569