Find parameter of distributions.

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question

Anutt K asked May 23 2023 at 3:15 AM Julie Weller commented May 30 2023 at 1:39 PM

Find parameter of distributions.

Hello. I wondering if in Expert Fit we can use to find Statistical Distribution from Raw Data.

So, If reverse. We know what type of Dristribution and quantity of Entity. Then we want to find parameter of distribution.

Exam. I have 250 Qty. of part in 1 hours and inter-arrival is Poisson distribution. So, How can I find Parameter (Mean of Poisson) to edit this case. Thank You.

Software Version:

FlexSim 22.2.0

distributions statistical distribution distribution parameters

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Answer 1 · 2023-05-24T14:08:31Z

Phil BoBo answered May 24 2023 at 2:08 PM Phil BoBo edited May 24 2023 at 4:24 PM

You don't need to use ExpertFit, OptQuest, or the Experimenter to solve your problem. The Poisson distribution is mathematically related to the Exponential distribution.

A poisson distribution describes the occurrences as a certain quantity per time period. An exponential distribution describes those same occurrences in terms of an inter-arrival time between occurrences (time per quantity). It's simply an inverse relationship.

"If for every t > 0 the number of arrivals in the time interval [0, t] follows the Poisson distribution with mean λt, then the sequence of inter-arrival times are independent and identically distributed exponential random variables having mean 1/λ." https://en.wikipedia.org/wiki/Poisson_distribution

If you have a Poisson distribution of "250 Qty. of part in 1 hours," then the scale (mean) parameter for the exponential distribution is 1/250 hours:

See also https://en.wikipedia.org/wiki/Exponential_distribution

1684937306822.png (131.0 KiB)

Answer 2 · 2023-05-24T06:54:21Z

Arun Kr answered May 24 2023 at 6:54 AM

Hi @Anutt K ,

You can set up an optimizer job or use the experimenter to find out a solution closer to your mean value which produces 250 items in 1 hour. This can also be done using trial and error in your simulation model.

First, you need to set up a simple source and sink. In the source set the inter-arrival time as the poison distribution and set the mean value as a parameter from the parameters table or a variable that you can experiment with. The stop time of the model is 1 hour. The parameter shall be of continuous variable type and select the range of values for the mean. Let the performance measure be the sink input.

If you plan to use the optimizer use minimize objective and set the performance measure with a constraint <=250 units. By changing the parameter range you will be able to find a mean value that is closer to producing 250 units in 1 hour.

Regards,

Arun KR

1684911250590.png (15.8 KiB)

Answer 3 · 2023-05-23T04:56:42Z

Joerg Vogel answered May 23 2023 at 4:56 AM Joerg Vogel commented May 24 2023 at 6:50 AM

Tool ExpertFit in Main Menu Statistics. But you get only parameters for a Poisson distribution, if your data fits. The tool suggest a best fitting distribution itself. On the other hand with just 250 events you can still use an empirical distribution from Toolbox.

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