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

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

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]]

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

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]]

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

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

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

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]]

David Winsemius, MD
Heritage Laboratories
West Hartford, CT

Sorry for the confusion.

Let me put it in this way. Here we have 2000 people and we want to put

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:

--------


-----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]]

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