# 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!

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