4
$\begingroup$

I'm a bit confused about the lambda value of a Poisson distribution. I know it means the average rate of success for a given interval. I'm confused about what this value exactly means through.

For example, If I have 2.4/100,000 people contracting a disease over a period of two years, what is the lambda value if I'm trying to figure out the probability of at least 5 cases of the disease out of 100,000 in one year? I'm not sure if it would be either 2.4/100,000 or 1.2/100,000 since the original average is over a period of two years. I'm also pondering if lambda could be 2.4 or 1.2 since the question already states a sample of only 100,000.

Thanks

$\endgroup$
8
$\begingroup$

Imagine we have a population of fixed size $100000$, say a small city. The "two year $\lambda$" is $2.4$. Then the "one year $\lambda$" is $1.2$.

You can think of it as follows. If the mean number of occurrences of the disease in a $2$ year period is $2.4$, then the mean number of occurrences in a $1$ year period is $1.2$.

Remarks: $1.$ Suppose we now change the city size to say $300000$. Then the appropriate $\lambda$ for a $1$ year period becomes $3.6$.

$2.$ For finishing your problem about at least five, it is easier to first find the probability that there are $4$ or fewer occurrences. This is $e^{-\lambda}\left(1+\lambda+\frac{\lambda^2}{2!}+\frac{\lambda^3}{3!}+\frac{\lambda^4}{4!}\right)$.

$\endgroup$
  • $\begingroup$ Last term should be 4!. I tried to edit it, but Stackexchange demands a minimum edit of 6 characters... :-/ $\endgroup$ – Pete Mancini Jun 15 '16 at 21:29
  • $\begingroup$ @PeteMancini: Thank you, I had missed the shift key. $\endgroup$ – André Nicolas Jun 16 '16 at 2:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for?Browse other questions tagged or ask your own question.