Physics307L:People/Mondragon/Poisson

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The desire to perform these experiments arose from arguments about how accurately a Poisson probability distribution could fit data that should most probably follow the Poisson distribution. One thing I see immediately is that the Poisson distribution can not fit data collected from a finite number of counting experiments exactly but as the number of counting experiments preformed approaches infinity, the data should fit the distribution more and more tightly.

I will be using the poissrnd() function included in Gnu Octave vers. 3.0.0 to generate random numbers with a Poisson distribution with parameter Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda} . Gnu Octave is open source, so it shouldn't be too difficult to find the source code and examine how these numbers are generated for those who are curious. I am using this number generator to model counting experiments.

Things I want to do:

  • using the Poisson random number generator, generate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle n} numbers using parameter Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda_0} and quantify
    • how well a Poisson distribution with parameter Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda_0} fits the generated data and how this varies with
    • what parameter for the Poisson distribution best fits the generated data and find a standard deviation for how much the parameter varies
  • repeat the above but with different . Try to find a relationship between , , and
  • for data generated with parameters and , find how accurate are the Poisson distribution's predictions of what the count frequency for count number is, and how this varies with , , and

For the test on how accurate the overall fit is, the dependent variable is and the independent variables are and . For the test of the accuracy of the distribution's predictions about the frequency of a count number, the dependent variable is and the independent variables are , and .

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