JSTOR Daily: Tables for Some Small Sample Tests of Significance for Poisson Distributions and 2×3 Contingency Tables
Tables for Some Small Sample Tests of Significance for Poisson Distributions and 2×3 Contingency Tables
1 I will give an intuitive explanation, only needing the defining properties of the Poisson Process and the exponential distribution, without needing any calculations involving densities. In short, the Poisson Process having independent and stationary increments and the exponential distribution being memoryless explains this connection:
The criteria in your book are for interval data; that would be useful if you had the dates at which hurricanes stroke... moreover these criteria are for constant rate Poisson processes, which is obviously (or I hope so) not the case of hurricanes. To check if your count data follow a Poisson distribution, a first elementary approach is the chi-square test.
How to know if a data follows a Poisson Distribution in R?
The number of cars appearing in a car park follows a Poisson distribution with a mean of 10 cars per hour. Find the probability of there being: (a) Exactly 5 cars in a 30 minute interval, (b) At most 3 cars in a 10 minute interval, (c) More than 4 cars in a 15 minute interval, (d) Exactly 1 cars in each of three consecutive 5 minute intervals.
Poisson distribution expresses the probability that a specific number of discrete independent events happen over a fixed time interval, as long as the events are sufficiently rare. To be precise, I
I think this "proof" is way too much. The memoryless property states that no interval is more likely than another with the same length to have an event and that probability of an event does not depend on past or future events. This is more than enough to prove that, given the number of events, the time distribution of those events in the interval is uniform.