Physics307L:People/Mondragon/Poisson

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 $$\lambda$$. 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 $$n$$numbers using parameter $$\lambda_0$$ and quantify
 * how well a Poisson distribution with parameter $$\lambda_0$$ fits the generated data and how this varies with $$n$$
 * what parameter for the Poisson distribution $$\lambda$$ best fits the generated data and find a standard deviation for how much the parameter varies
 * repeat the above but with different $$\lambda_0$$. Try to find a relationship between $$\lambda$$, $$\Delta\lambda$$, and $$n$$
 * for data generated with parameters $$\lambda_0$$ and $$n$$, find how accurate are the Poisson distribution's predictions of what the count frequency for count number $$k$$ is, and how this varies with $$k$$, $$n$$, and $$\lambda$$

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

This is to be the main branch page

From here, access
 * /Notebook
 * /Programming