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Tuesday, 29 December 2009

Poisson to digest at Christmas

I have had a few things to think about whilst digesting the Christmas fare.

Dan asked whether the data I presented about street robbery's likely victims and likely offenders is a Poisson distribution. My answer is "No it is not" because the whole point is that certain people are more likely than others by their demographic (and probably their geodemographic (we have yet to come to that)) characteristics to be victims and/or offenders. This means that the distribution is not random. The problem is it is not deterministic either therefore it can be argued that there is a degree of randomness.

To discuss this more practically time and location need to included as these are the other elements in the commission of a crime (a commodity to steal is possibly another element but in the present discussion this is assumed to be part of the victim's characteristics). I have shown that in the brief analysis of time and place that these factors appear not to be random either. There are specific times and specific places where crimes are more likely to occur than other times and places. So all four elements for a crime to occur are not random.

If on the other hand if a question is formed in such a way that the non-random elements become insignificant it may be possible to use a Poisson calculation or calculator to determine the likelihood of a crime occurring. For instance, if it were known that in a particular grid square an average (mean) of one street robbery occurred every week what is the probability of none, one, or two or more occurring in any one of the weeks? Using the calculator the answers are 37%, 37% and 26% respectively.

This is interesting. The degree to which the location, time, offender and victim are not random can be tested against a theoretical Poisson distribution....................

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