1. poisson approximation

i've been thinking about this for ages but just can't get it to work..any hints/advice would be very very much appreciated. i have a table of data on the number of deaths from a certain disease per year. there are 5 years given, and all of the death totals are around 3100..i calculated the mean to be 3158.6 and variance 3074.8. i've been asked to model the number of deaths per year by a poisson distribution..would the value for the lamda be 3158.6? i don't know what else it could be..but at the same time this would make all probabilities zero as e^-3158.6 is zero when used in the poisson formula. so it must be wrong? any help would be great..thank you

2. Originally Posted by rainbow
i've been thinking about this for ages but just can't get it to work..any hints/advice would be very very much appreciated. i have a table of data on the number of deaths from a certain disease per year. there are 5 years given, and all of the death totals are around 3100..i calculated the mean to be 3158.6 and variance 3074.8. i've been asked to model the number of deaths per year by a poisson distribution..would the value for the lamda be 3158.6? i don't know what else it could be..but at the same time this would make all probabilities zero as e^-3158.6 is zero when used in the poisson formula. so it must be wrong? any help would be great..thank you
Hi rainbow,

A Poisson distribution with a mean of 3158.6 is not necessarily wrong and may fit your data well, but it's difficult to work with from a practical point of view. For example, if you want the probability of exactly 3158 deaths, that would be given by
$e^{-3158.6} (3158.6)^{3158} / 3158!$
which is hard to compute. So although a Poisson distribution may be theoretically correct in this case, it's difficult to work with, and for that reason it would probably be better to use a normal distribution as an approximation.

By the way, it's not correct to say that e^-3158.6 is zero-- it's just very small (despite what your calculator may say).