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

Ravi Varadhan RVaradhan at jhmi.edu
Tue Nov 10 21:30:40 CET 2009


May be you are interested in the first `n' for which the sum of iid gamma
rvs exceeds 2000, subject to the min-max constraints on each rv. 

If so, the following one-liner will give it to you:

which(cumsum(pmax(1, pmin(rgamma(500, shape=0.067, rate=0.008), 85))) >
2000)[1]

Note that I have used a slightly inefficient code (a somewhat generous N of
500), but this permits economy of code (on-liner!).

Ravi.
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Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:
http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadhan.h
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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Hongwei Dong
Sent: Tuesday, November 10, 2009 2:57 PM
To: David Winsemius
Cc: R-help Forum
Subject: Re: [R] Generate Random Draw from Gamma Distribution Re: Monte
Carlo Simulation in R...

Thanks.
I tried the rgamma function too. But I'm still wondering how I can set the
min, max, and sum of the variates created by the random draws. Anyone has a
clue? Thanks.

Garry



On Tue, Nov 10, 2009 at 11:47 AM, David Winsemius
<dwinsemius at comcast.net>wrote:

>
> 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]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> David Winsemius, MD
> Heritage Laboratories
> West Hartford, CT
>
>

	[[alternative HTML version deleted]]

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