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

Ravi Varadhan RVaradhan at jhmi.edu
Tue Nov 10 22:57:49 CET 2009


If the number of groups can be set "endogenously" my previous email about
the smallest `n' would apply.  You can view this as a "waiting time"
problem.  Here is one approach:

x <- round(pmax(1, pmin(rgamma(500, shape=0.067, rate=0.008), 85)))

csx <- cumsum(x)

ind <- which(csx > 2000)[1]

xg <- c(x[1:(ind-1)], 2000 - csx[ind-1])  # group sizes

sum(xg)

length(xg)  # number of groups

However, note that the elements of `xg' are not gamma variables (due to
min-max constraint), and they are all not independent (due to sum
constraint).

Hope this helps,
Ravi.

----------------------------------------------------------------------------
-------

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
tml

 

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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 4:44 PM
To: R-help Forum
Subject: Re: [R] Generate Random Draw from Gamma Distribution Re: Monte
Carlo Simulation in R...

By the way, maybe the number of groups can be determined endogenously. It
will be better if I do not have to set the total number of groups
exogenously.

Thanks
Garry

On Tue, Nov 10, 2009 at 1:29 PM, Hongwei Dong <pdxdong at gmail.com> wrote:

> Sorry for the confusion.
>
> Let me put it in this way. Here we have 2000 people and we want to put
them
> into 150 groups. The distribution of the group size follows the Gamma
> distribution with shape parameter 0.067 and scale parameter 0.008. At the
> same time, the minimum group size is 1, and the largest one should not be
> bigger than 85.
>
> My questions:  Can I generate a set of groups that follow the above rules
> by generating random draws?
>
> By the way, I also confused by the rate and scale parameters in R. I did
> the distribution test in SPSS and got those shape and scale parameters. In
> SPSS Q-Q plot, the scale parameter is 0.008. I noticed that someone
> mentioned that this is actually the rate. I'm confused.
>
>
> Thanks a lot.
> Garry
>
>
>
>
> On Tue, Nov 10, 2009 at 12:15 PM, Ravi Varadhan <RVaradhan at jhmi.edu>wrote:
>
>> I think he means "rate = 0.008", so he is looking for:
>>
>>  rgamma(n, shape=0.067, rate=0.008)
>>
>> Even then his problem is not well-posed.  You cannot have both
>> "independent"
>> gamma rv's and have them sum to 2000.
>>
>> Ravi.
>>
>>
----------------------------------------------------------------------------
>> -------
>>
>> 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
>>
tml<http://www.jhsph.edu/agingandhealth/People/Faculty_personal_pages/Varadh
an.html>
>>
>>
>>
>>
>>
----------------------------------------------------------------------------
>> --------
>>
>>
>> -----Original Message-----
>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
>> On
>> Behalf Of David Winsemius
>> Sent: Tuesday, November 10, 2009 2:47 PM
>> To: Hongwei Dong
>> Cc: R-help Forum; Duncan Murdoch
>> Subject: Re: [R] Generate Random Draw from Gamma Distribution Re: Monte
>> Carlo Simulation in R...
>>
>>
>> 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
>>
>> ______________________________________________
>> 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.
>>
>>
>

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