[R] Generate Random Draw from Gamma Distribution Re: Monte Carlo Simulation in R...

[David Winsemius]

On Nov 10, 2009, at 2:26 PM, Hongwei Dong wrote:

> Exactly! Thanks, Duncan.
>
> Let me re-phrase me question like this:
>
> 1) X_i values are independent Gammas, with the shape 0.067 and scale  
> 0.008
> 2) Min(X)=1 and Max(X)=85

You might want to check that your parameterization in in agreement  
with that used by the rgamma function. Simply using those numbers  
yields a distribution that does not look as though it would get many  
qualifying samples. Here are 20 draws without any exclusions outside a  
range:

 >  rgamma(20, shape=0.067,  scale = 0.008)
  [1] 2.213459e-03 2.815705e-05 2.381306e-04 2.264602e-07 1.293713e-07  
7.680773e-38 6.441082e-15 6.168961e-13
  [9] 5.089033e-06 1.571858e-16 9.869878e-12 1.813121e-13 1.253287e-11  
1.852885e-04 4.212802e-07 1.774495e-25
[17] 1.892984e-07 5.927422e-17 1.322638e-12 4.327472e-05

http://finzi.psych.upenn.edu/R/Rhelp02/archive/31459.html


> 3) SUM(X)=2000
> 4) Do I also have to define the number of draws? if yes, it could be  
> 250.
>
> Based on these restrictions, I want to generate random draw. I'm  
> wondering
> how I can do this in R. Thanks.
>
> Garry
>
>
>
> On Tue, Nov 10, 2009 at 11:17 AM, Duncan Murdoch  
> <murdoch at stats.uwo.ca>wrote:
>
>> On 11/10/2009 1:25 PM, Hongwei Dong wrote:
>>
>>> Hi, Dear R users,
>>>
>>> I'm wondering if I can do Monte Carlo Simulation in R. My problem  
>>> is like
>>> this: I know variable X follows Gamma distribution with shape  
>>> parameter
>>> 0.067 and scale parameter 0.008. The sum of the X is 2000. I need  
>>> R help
>>> me
>>> to simulate a vector of X that satisfies both the probability  
>>> distribution
>>> and the sum. Anyone has a clue to this? Much appreciated.
>>>
>>
>> Your requirements are slightly contradictory or incomplete.  Here's  
>> one way
>> to fully specify the problem:
>>
>> The X_i values are independent Gammas, with the given shape and  
>> scale. You
>> want to simulate from the joint distribution conditional on the  
>> event sum(X)
>> == 2000.
>>
>> Is that your problem?  I don't know how to do the simulation, but  
>> maybe
>> someone else does.
>>
>> Duncan Murdoch
>>
>
> 	[[alternative HTML version deleted]]
>
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David Winsemius, MD
Heritage Laboratories
West Hartford, CT