Professeur Poisson still rules
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understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.
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We've previously shown that the number of homicides each day in London followed a Poisson distribution to a remarkable degree - this means that they essentially occur as a random process. Now the same analysis has been repeated by the Home Office in the crime statistics released today - and the Poisson fits very well.
The Home Office analysis covers homicide incidents for the whole of England and Wales over a three-year period. The figure below is from page 25 of Homicides, Firearm Offences and Intimate Violence 2009/10.
The number of days on which different numbrs of homicide incidents occur: England and Wales. The 'expected' is a Poisson distribution
This finding allows proper checks of changes in homicide rate, as well as showing that days are bound to occur when there are apparently a cluster of incidents: to quote the report: For example, from knowing there is an average of 1.78 incidents a day it was predicted that, over the period of 1,096 days, there would be 27 days on which there would be exactly five independent incidents. The observed number was 26, indicating that the occurrence of these apparent ‘clusters’ is not as surprising as one might anticipate.
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