[R] R code for the MLE of a geometric distribution

[Bill.Venables at csiro.au]

This is an imprecise question.

There are actually two geometric distributions.  See
http://en.wikipedia.org/wiki/Geometric_distribution

They are related, of course.  One is defined as the minimum number of
trials to achive one success in bernoulli trials.  The other is the
number of failures preceding the first success in bernoulli trials.  The
second is the more convenient for most applications.  Let's assume this
is your definition. If not, just subtract 1 from all your data.

If you are talking about the maximum likelihood estimate of "the"
parameter of a geometric distribution, it suggests you are dealing with
a homogeneous sample.  In this case you don't need much R code.  There
is a formula for the MLE which you can simply compute. (See, e.g. the
above link).  Anyone using R should be able to do that.

If the situation is more complex and you are dealing with a generalized
linear model where the data are geometric (in the second sense above)
with the mean related to a linear function of predictors using a link
function, then you have a much more interesting case.  One way to do
this is to use the fact that the geometric distribution is a special
case of the negative binomial:

require(MASS)
modl <- glm(y ~ x1+x2+..., 
  family = negative.binomial(theta = 1),  ### i.e. the Geom. Dist.
    data = myData, ....)

and all the paraphernalia of generalized linear modelling then apply.


Bill Venables.


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Kathy Maher
Sent: Sunday, 16 March 2008 12:26 PM
To: R-help at r-project.org
Subject: [R] R code for the MLE of a geometric distribution

Does anyone know how to approach R code for the MLE of a geom.
distribution?

thanks!