Describe the sampling distribution of the maximum likelihood estimator...

• October 21st 2009, 04:11 AM
chella182
Describe the sampling distribution of the maximum likelihood estimator...
Okay, I literally have no idea with this, so I'm just gonna give you all the info I have and see if anyone can help. (I've attached the PDF with my whole assignment on, but this post's referring only to section A, question 1 part a).

Describe the sampling distribution of the maximum likelihood estimator for the Geometric parameter $\pi$ for samples of size 5 obtained from a Geom(0.01) distribution.

Now basically this question involes a program called R (don't know how many people know what it is) and I've typed the following code in...

m<-1000
n<-5
gsim<-matrix(nrow=n,ncol=m)
for (i in 1:m)
{
gsim[,i]<-rgeom(n,0.01)
}
gmle<-vector()
for (i in 1:m)
{
gmle[i]<-1/(mean(gsim[,i])+1)
}
hist(gmle)

...where m is the number of data sets, n is the size of said data sets, and this is all from the Geom(0.01) distribution, so $\pi=0.01$. It might also be useful to tell you that we're using $Pr(X=x)=(1-\pi)^{x}\pi, x=0,1,2,...$ as well, as apparently this is the Geometric distribution favoured by R.
The histogram I obtain from running all of the above code is attached to the post (any code I type in will be in Courier New).

So yeah, does anyone have any idea what the question means? I thought it was asking for a comment on what the histogram looks like, but that's parts (c) and (d), not (a) (Worried) I think I've given all the information needed... I've given everything I have written here, anyway.
• October 21st 2009, 04:57 AM
mr fantastic
Quote:

Originally Posted by chella182
Okay, I literally have no idea with this, so I'm just gonna give you all the info I have and see if anyone can help. (I've attached the PDF with my whole assignment on, but this post's referring only to section A, question 1 part a).

Describe the sampling distribution of the maximum likelihood estimator for the Geometric parameter $\pi$ for samples of size 5 obtained from a Geom(0.01) distribution.

Now basically this question involes a program called R (don't know how many people know what it is) and I've typed the following code in...

m<-1000
n<-5
gsim<-matrix(nrow=n,ncol=m)
for (i in 1:m)
{
gsim[,i]<-rgeom(n,0.01)
}
gmle<-vector()
for (i in 1:m)
{
gmle[i]<-1/(mean(gsim[,i])+1)
}
hist(gmle)

...where m is the number of data sets, n is the size of said data sets, and this is all from the Geom(0.01) distribution, so $\pi=0.01$. It might also be useful to tell you that we're using $Pr(X=x)=(1-\pi)^{x}\pi, x=0,1,2,...$ as well, as apparently this is the Geometric distribution favoured by R.
The histogram I obtain from running all of the above code is attached to the post (any code I type in will be in Courier New).

So yeah, does anyone have any idea what the question means? I thought it was asking for a comment on what the histogram looks like, but that's parts (c) and (d), not (a) (Worried) I think I've given all the information needed... I've given everything I have written here, anyway.

This looks like an assignment that counts towards your grade. MHF policy is to not knowingly provide help with such questions. They are meant to be your own work. Thread closed.