observations. This rate is held constant in Poisson, but varies in
Negative Binomial.
Can we interpret the value of lambda literally, i.e. lambda = 1 --> one
event per time period, lambda = 10 --> ten observations per time period,
etc? I guess we need to understand this to select an appropriate range
for lambda..
Thanks,
Stan
****************************
Stanislav Markus
Ph.D. Candidate
Harvard University
Department of Government
e: smarkus(a)fas.harvard.edu
t: 617.513.5407
-----Original Message-----
From: gov2001-l-admin(a)fas.harvard.edu
[mailto:gov2001-l-admin@fas.harvard.edu] On Behalf Of Kosuke Imai
Sent: Wednesday, February 26, 2003 11:27 AM
To: Olivia Lau
Cc: gov2001-l(a)fas.harvard.edu
Subject: Re: [gov2001-l] Problem 4
You are right that gamma is a continuous distribution. So, you have to
discretize it by creating a sequence of values for an appropriate range
of
lambda. Then, you can create a matrix (in R) where its i,j element
represents the joint density evaluated at the ith value of Y and the jth
value of lambda. Now, if you sum over the column (or "scoop" to use
Gary's
word), you will obtain the marginal density of Y. Is that clear now?
Kosuke
On Wed, 26 Feb 2003, Olivia Lau wrote:
> I think that the confusion is this: If lambda is distributed
> according to the gamma (continuous) distribution, how can we
> "construct a matrix"? Do you really want us to construct an
> actual matrix (in R), for which (I think) we would need to
> evaluate the poisson distribution at specific values of lambda,
> or do you just want us to do it theoretically and integrate to
> get the marginal density over some range of y?
>
> Am I still lost?
>
> Thanks, Olivia.
>
> ----- Original Message -----
> From: "Kosuke Imai" <kimai(a)fas.harvard.edu>
> To: <gov2001-l(a)fas.harvard.edu>
> Sent: Wednesday, February 26, 2003 9:57 AM
> Subject: [gov2001-l] Problem 4
>
>
> > A number of people have asked questions about problem 4 last
> night. Here
> > is a basic idea. You want to evaluate the "joint" density with
> different
> > values of y and lambda where y is poisson and lambda is gamma.
> This is the
> > joint density function, so you are not drawing random
> variables from any
> > distribution. you are simply evaluating the height of the
> density. To do
> > this, you need to create a matrix where its row and column
> represents y
> > and labmda, respectively. Then, to integrate out lambda, you
> want to sum
> > over the column. After normalizing it, this gives you the
> marginal
> > density of negative binomial.
> >
> > Kosuke
> >
> > _______________________________________________
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> > gov2001-l(a)fas.harvard.edu
> > http://www.fas.harvard.edu/mailman/listinfo/gov2001-l
> >
>
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