Mode of Poisson distribution

**jlt1209** · August 28th 2010, 09:35 AM

Find the mode of a P(lamda) distribution.

I believe that where lamda is not an integer, the mode is floor(lamda) (largest integer <= lamda) and where lamda is a positive integer, the mode is lamda and lamda-1, but can someone help explain how to get to this point ... I can't seem to figure out how to get to these values.

Thank you!

**mr fantastic** · August 28th 2010, 01:59 PM

Originally Posted by jlt1209

Find the mode of a P(lamda) distribution.

I believe that where lamda is not an integer, the mode is floor(lamda) (largest integer <= lamda) and where lamda is a positive integer, the mode is lamda and lamda-1, but can someone help explain how to get to this point ... I can't seem to figure out how to get to these values.

Thank you!

Hint: $\displaystyle \frac{\lambda^n}{n!} \geq \frac{\lambda^{n-1}}{(n-1)!}$ provided $\displaystyle \frac{\lambda}{n} > 1$ .

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