On Nov 10, 2009, at 5:00 PM, David Winsemius wrote:
On Nov 10, 2009, at 4:29 PM, Hongwei Dong 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.
I think you may want your scale (from whatever dataset it was
determined) to be 1/0.008
Note that Ravi Varadhan and I may not be not disagreeing since:
> rgamma
function (n, shape, rate = 1, scale = 1/rate)
snipped
You are fairly far out in the right tail of that distribution:
> round(rgamma(200, shape=0.067, scale = 1/0.008))
[1] 12 0 0 0 20 0 9 0 54 0 0 0 2 8 49
0 26 0 0 0 0 2 0 0 0 0
[27] 0 0 3 0 0 1 0 0 0 11 0 0 1 256 0
3 0 9 0 0 0 0 0 1 0 0
[53] 0 0 0 0 1 0 0 0 2 1 0 0 0 0 13
0 0 0 0 0 0 0 152 157 0 3
[79] 4 0 0 0 0 26 0 34 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
[105] 4 0 0 0 0 0 0 0 2 0 1 0 5 2 0
18 0 0 0 0 0 0 19 0 190 0
[131] 0 0 2 0 0 0 0 83 0 0 0 0 0 4 0
0 0 0 0 20 0 9 1 1 0 0
[157] 0 4 16 0 28 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 23 0 0
[183] 0 0 0 0 6 1 1 0 1 0 0 0 1 0 0
0 0 0
I'm wondering if the Gamma distribution is the correct distribution to
be fitting? Is there some sort of
--
David
Read this message on an SPSS mailing list:
http://www.listserv.uga.edu/cgi-bin/wa?A2=ind9902&L=spssx-l&D=0&F=P&P=7633
.... and then look at the parameterization for rgamma in the r help
pages. I seem to remember that Terry Therneau has also pointed out
this ambiguous scale parameter issue for gamma in the past.
(This is, by the way, beginning to sound quite a bit like a homework
problem.)
--
David
Thanks a lot.
Garry
On Tue, Nov 10, 2009 at 12:15 PM, Ravi Varadhan <rvarad...@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.
-----Original Message-----
From: r-help-boun...@r-project.org [mailto:r-help-boun...@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
<murd...@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
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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