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Re: [Phys-l] Dog attacks and the Poisson interval distribution


On 2012, Mar 08, , at 15:41, brian whatcott wrote:

bc,

You have asked twice for comments on your killer dog survey.
Not all your assertions are supported.
For example:

"there are many factors that cause an attack"
Really? What would these be?


Teasing of the dog, abuse by the owner, training to attack strangers, bad lunch, no lunch, genetic?, victims smells from fear, etc.


"the number of attacks is infrequent,...."
Attacks are infrequent or the number of attacks is small.


Grammar!


"the possibility of attack is high"
Arguably, "possibility is a binary quantity: possible or impossible.


Again poor choice of word. Opportunity is high. (great?)


"(very frequent dog person interactions)"
You have no evidence to this datum.


Come now -- many were children of the owners. How about the daily (except Sunday and soon Saturday) visit by the USPS, plus UPS, and FedX carriers?




"That it is a rare event is simply because pit bull attacks are rare"
Dog-killings are rare because dog-killings are themselves rare??


No; three in one day in a city is rare because attacks are rare.


"the number of events increases exponentially with decreasing time
interval. (time between the events)"
It's possible you meant that if the time between events is reduced,
their number accumulates faster.
That is not what you wrote, however.


thanks -- My Alzheimer's prevented me from being more felicitous.


"To test that dog bites observe a Poisson distribution"
You are not discussing dog-bites, but rather dog-caused deaths.


I suggested that they are related? Or one is supposed to presume this,


Finally, some of the URLs that BC offered were not accessible to me.


Others have that difficulty?

Hope that is helpful.

Brian W



Again thanks.

p.s. Again I made an assumption that twice disembodied was OK: H. sapiens deaths => H. s attacks => animal attacks.


On 3/8/2012 10:20 AM, Bernard Cleyet wrote:
Phys-lers!

Here's an analysis I'm sending to the staff writer of the three recent dog biting incidents in Salinas Am I all wet, or is it cogent? -- before I send it off, your critique.


bc


People!

Animal control officers characterize the three pit bull attacks in Salinas* on the same day as a statistical anomaly. This is not true! That it is a rare event is simply because pit bull attacks are rare, especially if in a small area, e.g. a city.

Dog attacks are random, because there are many factors that cause an attack. Therefore, the central limit theorem applies.** Because , and they are random and unrelated, the Poisson distribution applies. A corollary of that distribution is the Poisson interval process,*** which is, the interval between events is an exponential function, i.e. the number of events increases exponentially with decreasing time interval. (time between the events)


A common method of determining, if infrequent, but very possible (not probable) events observe the Poisson distribution is to plot the event number in each of increasing intervals. This is, for example, a method used to test the functioning of a nuclear radiation detector using a radioactive source.

To test that dog bites observe a Poisson distribution
, and show the dog bite animal Salinas events were not anomalous, I analyzed the data of dog bite fatalities**** over the three years 2009=>2011 as reported by the media in the US. Because there were about 75 fatalities in the three year period, I grouped the data in successive seven day intervals. The plot is here:

The time interval between fatalities:

Fatal dog attacks 3 years seven day intervals.tiff 1,168×738 pixels


http://www.cleyet.org/Someone_is_Wrong/Multiple%20single%20day%20dog%20attacks%20are%20not%20anomolous/Fatal%20dog%20attacks%203%20years%20seven%20day%20intervals.tiff



bc forgot all three attacked were animals, tho in one case the dog threatened an officer, hence this makes multiple same day in the same city attacks even more likely! And he reads the newspaper.

http://www.ams.org/notices/199603/comm-kolata.pdf


Bernard Cleyet, PhD

http://www.cleyet.org/


Foot Notes:


* Pit bull attacks common, animal control officers say - MontereyHerald.com :


http://www.montereyherald.com/ci_20064947/pit-bull-attacks-common-animal-control-officers-say?source=most_viewed


** Central limit theorem - Wikipedia, the free encyclopedia

http://en.wikipedia.org/wiki/Central_limit_theorem



*** Poisson process - Wikipedia, the free encyclopedia


http://en.wikipedia.org/wiki/Poisson_process


**** I didn't find by Googling quickly just dog attacks, so I used the fatality data. (next URL) I suspect only a small proportion of attacks result in death, and since several fatalities occurred on the same day, it's not very unlikely that multiple attacks would occur in the same city on the same day.

List of fatal dog attacks in the United States - Wikipedia, the free encyclopedia


http://en.wikipedia.org/wiki/List_of_fatal_dog_attacks_in_the_United_States

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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l