# Poisson Distribution

There are four criteria for a Poisson distribution. These are:

1) you are counting with integers the number of times an event happens in an area of opportunity (time span, area of land, length of road, etc). So I could be counting the number of poetry submissions made to my Mused Literary Magazine for the three month submission cycle.

2) The probability of an event occurring in one part of this area is the same as for all parts of this area. So submission rates would need to be the same in month 3 as they are in month 1.

3) The number of times an event happens in one area is independent to the event happening in another area. So one person submitting on Jan 1 can't then cause 800 other people to suddenly submit.

4) The probability of two or more events happening simultaneously becomes zero as you focus in on a given area. So it's unlikely that two poems will get submitted at the exact same nanosecond.

In terms of difficulty:

#1 - Fairly easy. Hopefully if you are doing this exercise in the first place you have a sense of what you want to count and for what area.

#2 - Challenging. With my Mused Literary Magazine, submissions are fairly quiet at the beginning of the cycle. Then during the last week - which we're in right now - we start to get flooded. Our deadline for submissions is this coming Fri Feb 4th and we'll be deluged on that day as everyone scrambles to get their submissions in on time. So for Mused if I wanted to do this kind of evaluation I'd want to study "down-time submissions" (months 1 and 2) since during those periods they are quiet and steady. Even their example in the book about lunch hour, I disagreed with. They claimed that everyone would come in equally across a lunch hour. However if we assume that they are looking at 12-1pm, and that most people in the area have lunch from 12-1, that would mean it's quiet at the beginning as people had to physically leave their offices. Then it'd be busy in the middle, and then it'd be quiet near the end because everyone had to account for travel time to get back to their offices. So I would have done that study for the middle 1/2 hour of lunch time.

#3 - Fairly easy. For most things, the events won't be affected by other events. Mused entries are completely blind. Nobody knows who else has submitted or when or so on. So if person X submits 2 poems, it won't have any effect on person Y deciding this is the day to submit their two poems. I can of course think up situations where the events DO effect each other. For example, people are less likely to eat in an empty restaurant. It makes them wonder if the food is any good. So if you have an empty restaurant at lunch hour, the probability is low that the first person will go in and sit down. But now let's say you have two tables of people in the front windows (which is where restaurants tend to put the first arrivals, to lure others in). Now other people will go past, see those people, and be more likely to go in as well. So those first events does actually have an effect on subsequent events happening.

#4 - Fairly easy. For most things, as you select down to tiny time or land increments the chance of two things being on top of each other becomes more slim. My Mused database can only physically write one record to the hard disk at a time, so even if two did somehow miraculously try to come in at the exact same time one record would still wait its turn in line to be written until the previous one was done.

Statistics Basics