How do I change a poisson spreadsheet into a bivariate version?

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SUMMARY

This discussion focuses on modifying an Excel spreadsheet that currently utilizes a Poisson distribution to calculate the probability of correct soccer scores, transitioning to a bivariate Poisson distribution. The key takeaway is that if the two variables are independent, their Poisson distributions can be multiplied. However, if they are not independent, understanding the correlation is crucial. Additionally, the draw probability must be incorporated into the calculations to ensure accurate results, as the initial attempts yielded lower probabilities than actual outcomes.

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  • Understanding of Poisson distribution and its applications in probability.
  • Familiarity with Excel functions for statistical calculations.
  • Knowledge of bivariate distributions and correlation concepts.
  • Ability to interpret and manipulate probability parameters in statistical models.
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  • Research how to implement bivariate Poisson distribution in Excel.
  • Learn about calculating correlation coefficients and their impact on distributions.
  • Explore methods for incorporating draw probability into Poisson distributions.
  • Study advanced statistical modeling techniques for soccer match predictions.
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Data analysts, statisticians, and sports analysts looking to enhance predictive models for soccer match outcomes using advanced statistical methods.

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I have an excel spreadsheet that uses poisson to figure out the probability of correct scores in soccer matches.

How do I amend the spreadsheet to use a bivariate poisson distribution?
 
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If the two variables are independent, just multiply the Poisson distributions of each. If they are not independent, what information about the correlation do you have?
 
HallsofIvy said:
If the two variables are independent, just multiply the Poisson distributions of each. If they are not independent, what information about the correlation do you have?

1. There is additional restriction - draw probability as parameter for distribution. Draw - this is the case when M(t) = N(t).
In common Pdraw = sum(M(ti)*N(ti)), i = 0, 1, 2 ...

2. I have tried to multiply the Poisson distributions of each for calculation the spreadsheet, but calculated Pdraw is lower than fact Pdraw. And calculated data don't correlate with fact data. Results from this that I don't take into account some factors (first of all, draw probability), which shall correct Poisson distribution.

How I can take into account draw probability to modificate the Poisson distribution?
 

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