Answer to Question #259702 in Economics for Nee

Question

PROBLEM:

Suppose a sample x₁, ..., x_n is modelled by a Poisson distribution with parameter denoted λ, so that

 

 

(a)   Restate the likelihood function of a Poisson distribution

 

(b)  Prove that the natural log likelihood function of the Poisson distribution i.e. show that you arrive at this log function.

 

(c)   Expand, rearrange, and take first derivate and show that you arrive at the function below

(d)  Find the maximum likelihood function (Hint: make equation in (c) equal to 0.

 

(e)   Let us assume a dataset with n= 647 and the observed frequencies of domestic accidents are as follows

 

Number of accidents Frequency

0 447

1 132

2 42

3 21

4 3

5 2

Using the Poisson distribution, calculate the MLE for λ i.e. prove that MLE for λ is 0.465.

Answer 1

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