Author 
Comment/Response 
William Duhe

07/30/13 10:56pm
With the code bellow; What I want to do is get the probability density of the list generated by S1[\[Alpha,off], plot it in a Histogram and then fit that with a Gaussian curve and extract the statistics. The key quantities I'm looking for in the table are the mean and RMS of the distribution you get, and the chisq / NDF of the fit to the unit Gaussian.
off = 1000;(*Expected Number of Off Counts*)
\[Alpha] = .01;(*Ratio of On/Off Counts*)
Non = 1000;
Noff = RandomVariate[PoissonDistribution[off], 10000];
(*Normal Distribution*)
h2 = Plot[PDF[NormalDistribution[], x], {x, 6, 6},
PlotStyle > Directive[Red, Thick]];
Attributes /@ {Greater, Sign}
{{Protected}, {Listable, NumericFunction, Protected, ReadProtected}}
S1[off_, \[Alpha]_] =
Sign[Non  \[Alpha]*Noff]*
Sqrt[2] (Non*Log[(1 + \[Alpha])/\[Alpha] (Non/(Non + Noff))] +
Noff*Log[(1 + \[Alpha]) (Noff/(Non + Noff))])^(1/2);
ListPlot[S1[off, \[Alpha]], Frame > True, Axes > False,
PlotLabel > "Formula 17"]
hist22 = Histogram[S1[off, \[Alpha]], 26, "ProbabilityDensity",
PlotLabel > "Formula 17", AxesLabel > "Probability"];
Show[hist22, h2]
URL: , 
