Poisson distribution on a simulated (SSA) data set

[tolove]

I've been asked to fit the histogram with a Poisson distribution as part of a mostly independent learning thing. The data was produced through a stochastic simulation.

Can someone get me started on how I would go about finding the expected distribution?

If you need additional information, or if you would like to see the code (python), please ask.

Thanks for your time!

 

[bpet]

If your data is coming from time-series observations, then perhaps a more important question is *should* you be fitting the data directly to a distribution?

 

[tolove]

If your data is coming from time-series observations, then perhaps a more important question is *should* you be fitting the data directly to a distribution?

That's what I'm thinking, but I was specifically asked to set a Poisson distribution to this. So there must be a way that the propensities can be used to find a prediction. Or at least a close approximation for long times.

I don't know how to go about this, though.

 

[FactChecker]

That's what I'm thinking, but I was specifically asked to set a Poisson distribution to this. So there must be a way that the propensities can be used to find a prediction. Or at least a close approximation for long times.

I don't know how to go about this, though.

The mean of the sample approximates the λ parameter of the Poisson distribution. That defines the Poisson distribution. My guess is λ ~ 8.

 

[blue_raver22]

I am happy to assist you with fitting a Poisson distribution to your simulated data set. The first step in finding the expected distribution is to understand the characteristics of a Poisson distribution and how it relates to your data. The Poisson distribution is a discrete probability distribution that is commonly used to model the occurrence of rare events. It is often used in situations where the number of occurrences of an event is known, but the exact timing of the events is random. In your case, the stochastic simulation likely produced a data set where the number of occurrences of a particular event is known, but the timing of each occurrence is random.

To fit the histogram with a Poisson distribution, you will need to use statistical software or programming language to calculate the parameters of the distribution. In Python, you can use the "scipy.stats" module to access the Poisson distribution and its associated functions. The two main parameters of the Poisson distribution are the mean (λ) and the standard deviation (σ), which can be calculated from your data set using the following formulas:

λ = mean of the data set
σ = square root of the mean of the data set

Once you have calculated these parameters, you can use them to generate a Poisson distribution and compare it to your simulated data set. If the distribution fits well, the histogram and the Poisson distribution curve should be similar.

It is important to note that fitting a distribution to your data is not a perfect process and it is possible that the Poisson distribution may not be the best fit for your data. If this is the case, you may need to explore other probability distributions and compare their fit to your data.

I hope this helps get you started on fitting a Poisson distribution to your simulated data set. If you need any additional assistance or would like to share your code for further feedback, please do not hesitate to ask. Best of luck with your independent learning project!