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Determining Lambda for a Poisson probability calculation [Solved!]

My question

I want to apply the Poisson distribution on highway robberies and highway accidents events to predict the probability of events. For this I would calculate the average of daily events occurring during the previous 10 days, to obtain ? and factor it into the Poisson formula.

The objective would be to calculate the Poisson P(X ?1) of an event (or more) occurring the next day (after the 10-day period.

I have reasons to believe that the latest values in the 10 day period are more representative than the older values. To add accuracy to ? and to calculate the Poisson cumulative probability for the next days (day by day), I can do one of the following two:

1) Take the previous 10 daily values and divide it by 10 to find ?. I would do this to calculate every “next day” lambda. This would be akin to calculating the moving average of a 10-day period, as the latest value will be added to the sequence and the last one would be dropped on every new 10-day sequence.

2) I would calculate the EMA-Exponential Moving Average of the same 10-day period to calculate the new ? and calculate the Poisson probability of highway robberies/accidents I should expect occurring in the next day (11th day).

QUESTION: Which of the two would you apply? Would it violate the premises of the Poisson distribution in any way?

Thank you very much!

Relevant page

Poisson Distribution Calculator

What I've done so far

I have carried out the processes described in 1) and 2)
I am looking for a second expert opinion.

X

I want to apply the Poisson distribution on highway robberies and highway accidents events to predict the probability of events. For this I would calculate the average of daily events occurring during the previous 10 days, to obtain ? and factor it into the Poisson formula.

The objective would be to calculate the Poisson P(X ?1) of an event (or more) occurring the next day (after the 10-day period.

I have reasons to believe that the latest values in the 10 day period are more representative than the older values. To add accuracy to ? and to calculate the Poisson cumulative probability for the next days (day by day), I can do one of the following two: 

1) Take the previous 10 daily values and divide it by 10 to find ?. I would do this to calculate every “next day” lambda. This would be akin to calculating the moving average of a 10-day period, as the latest value will be added to the sequence and the last one would be dropped on every new 10-day sequence. 

2) I would calculate the EMA-Exponential Moving Average of the same 10-day period to calculate the new ? and calculate the Poisson probability of highway robberies/accidents I should expect occurring in the next day (11th day). 

QUESTION: Which of the two would you apply? Would it violate the premises of the Poisson distribution in any way?

Thank you very much!
Relevant page

<a href="https://stattrek.com/online-calculator/poisson.aspx">
	Poisson Distribution Calculator
</a>

What I've done so far

I have carried out the processes described in 1) and 2)
I am looking for a second expert opinion.

Re: Determining Lambda for a Poisson probability calculation

@Aetius: I don't claim to be an expert in this area. My overall feeling is that if you want a better predictor, the best way would be to run the 2 experimental approaches side by side for a period of time (and/or using historical records), and see which is best at predicting the number for the next time period.

Statistics is really about trying to describe what's going on with numbers, so I wouldn't worry too much about "violating the premises of the Poisson distribution", but the experts may disagree!

Sorry I couldn't be more help.

X

@Aetius: I don't claim to be an expert in this area. My overall feeling is that if you want a better predictor, the best way would be to run the 2 experimental approaches side by side for a period of time (and/or using historical records), and see which is best at predicting the number for the next time period.

Statistics is really about trying to describe what's going on with numbers, so I wouldn't worry too much about "violating the premises of the Poisson distribution", but the experts may disagree!

Sorry I couldn't be more help.

Re: Determining Lambda for a Poisson probability calculation

Hello Murray!

Your suggestion is EXACTLY what I had intended to do, but welcome the input from others.
Thanks!

X

Hello Murray!

Your suggestion is EXACTLY what I had intended to do, but welcome the input from others.
Thanks!

Reply

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