Re: Find MLE for poisson(a)

From: Jack Tomsky <jtomsky@xxxxxxxxxxxxx>
Date: Mon, 10 Oct 2005 18:47:32 EDT

> have X_1,X_2,...,X_n. am supposed to estimate
> tau(a)=e^-a
>
> two parts:
> show that mle for a is x_bar.
> -just take the product from 1 to n of the standard
> poisson pdf. then take log of L(a) and the derivative
> equate 0 yields a_mle=x_bar
>
> is that correct?
>
>
> the second part is to find the expected value and
> varians of the following estimator for tau(a):
> 1.e^-X_bar
>
> how do i find the expected value and varians of an
> estimator? normally the expected value and varians of
> a poisson distribution is just a.

Here are some hints for you to carry out the details.

If Xi ~ Pois(x; a), then T = Sum(xi) ~ Pois(t; na).

The statistic for which you're interested in obtaining the mean and variance is exp(-t/n).

To get the expected value, multiply exp(-t/n) by the Poisson probability Pois(t, na), and sum from t = 0 to n.

Use the identity, Sum(y^t/t!) = exp(y).

The variance calculation uses a similar approach.

Jack
.

References:
- Find MLE for poisson(a)
  - From: grimster

Prev by Date: Re: The illusion of the bootstrap technique
Next by Date: Re: Applying Poisson methods
Previous by thread: Find MLE for poisson(a)
Index(es):
- Date
- Thread

Relevant Pages

Re: Suggestion Wanted: CI of Poisson times Gamma RV
... > I have a Poisson random variable, representing the number of defects ... My estimator is this Poisson RV, ... > I want to find confidence intervals (or the distribution) for this ...
(sci.stat.math)
Find MLE for poisson(a)
... show that mle for a is x_bar. ... the second part is to find the expected value and varians of the following estimator for tau: ... Prev by Date: ...
(sci.stat.math)