Poisson Maximum Likelihood in Excel

data_science

#1

Can any one please help me to find the MLE (Lambda) for Poisson distribution using excel?

It is not hoemwork question , i just want to see the likelihood for each data , here is question

“Suppose that the lifetime of Badger brand light bulbs is modeled by an exponential distribution
with (unknown) parameter λ. We test 5 bulbs and find they have lifetimes of 2, 3,1, 3, and 4 years, respectively. What is the MLE for λ?”

I can solve it using derivative function

f(2, 3, 1, 3, 4 | λ) = λ^5 e^−13λ
ln(f(2, 3, 1, 3, 4 | λ) = 5 ln(λ) − 13λ
Finally we use calculus to find the MLE:
d/dλ(log likelihood) = 5/λ - 13 = 0 ⇒ λˆ =5/13

How can i do the same in excel ?

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#2

If you solve this for a general sample with size n the MLE of lambda will come out to be inverse of mean for all the samples. Instead of trying to find dervative just calculated 1/mean.