Date: Jul 18, 2013 2:44 AM Author: Bob Hanlon Subject: Re: How to combine an If statement with Statistics

off = 140;(*Expected Number of Off Counts*)

=E1 = .3;(*Ratio of On/Off Counts*)

Non = RandomVariate[PoissonDistribution[=E1*off], 100000];

Noff = RandomVariate[PoissonDistribution[off], 100000];

(*Normal Distribution*)

h2 = Plot[

PDF[NormalDistribution[], x],

{x, -6, 6},

PlotStyle -> Directive[Red, Thick]];

Attributes /@ {Greater, Sign}

{{Protected}, {Listable, NumericFunction, Protected, ReadProtected}}

Non - =E1*Noff is a list and is neither positive nor negative. Note that

Greater is not Listable but Sign is Listable.

Clear[S2];

S2[off_, =E1_] =

Sign[Non - =E1*Noff]*

Sqrt[2] (Non*Log[(1 + =E1)/=E1 (Non/(Non + Noff))] +

Noff*Log[(1 + =E1) (Noff/(Non + Noff))])^(1/2);

ListPlot[S2[off, =E1],

Frame -> True,

Axes -> False,

PlotLabel -> "Formula 17"]

hist2 = Histogram[S2[off, =E1],

"Log",

"ProbabilityDensity",

PlotLabel -> "Formula 17 LOG"]

hist22 = Histogram[S2[off, =E1],

Automatic,

"ProbabilityDensity",

PlotLabel -> "Formula 17"];

Show[hist22, h2]

ProbabilityScalePlot[S2[off, =E1],

"Normal",

PlotLabel -> "Formula 17"]

Bob Hanlon

On Wed, Jul 17, 2013 at 1:50 AM, William Duhe <wjduhe@loyno.edu> wrote:

> Bellow is a code which attempts to change the sign (+/-) of S with an if

> statement. S1 is shown and S2 is the attempt to include the if statement.

>

> You can see from the information yielded from S1 that the Gaussian fit is

> off by roughly a factor of 2 when it should in theory match. This is

> because it is overestimating positive events due to the lack of the sign

> change. The sign change should change with the quantity I have assigned t=

he

> label "Signal". When the Signal is positive S2 should be positive and whe=

n

> Signal is negative S2 should become negative.

>

>

> (*VARIABLES*)

>

> Non = RandomVariate[PoissonDistribution[\[Alpha]*off], 100000];

> Noff = RandomVariate[PoissonDistribution[off], 100000];

> off = 140; (*Expected Number of Off Counts*)

> \[Alpha] = .3; (*Ratio of On/Off Counts*)

>

> (*Normal Distribution*)

> h2 = Plot[

> Evaluate@

> Table[PDF[NormalDistribution[0, \[Sigma]], x], {\[Sigma],

> 1}], {x, -6, 6}, PlotStyle -> Red];

>

> (*Signal*)

> S[off_, \[Alpha]_] = Non - \[Alpha]*Noff;

> hist = Histogram[S[off, \[Alpha]], Automatic, "ProbabilityDensity",

> PlotLabel -> "Signal"]

>

>

>

> (*Formula WITHOUT IF STATEMENT*)

> S1[off_, \[Alpha]_] = .5 Sqrt[

> 2] (Non*Log[(1 + \[Alpha])/\[Alpha] (Non/(Non + Noff))] +

> Noff*Log[(1 + \[Alpha]) (Noff/(Non + Noff))])^(1/2);

> ListPlot[S1[off, \[Alpha]], PlotLabel -> "Formula 17",

> PlotRange -> {{0, 100000}, {0, 8}}]

> hist1 = Histogram[S1[off, \[Alpha]], "Log", "ProbabilityDensity",

> PlotLabel -> "Formula 17 LOG"]

> hist11 = Histogram[S1[off, \[Alpha]], Automatic, "ProbabilityDensity",

> PlotLabel -> "Formula 17"]

> Show[hist11, h2]

> ProbabilityScalePlot[S1[off, \[Alpha]], "Normal",

> PlotLabel -> "Formula 17"]

>

>

>

>

> (*Formula WITH IF STATEMENT*)

> S2[off_, \[Alpha]_] =

> If[Non - \[Alpha]*Noff > 0,

> Sqrt[2] (Non*Log[(1 + \[Alpha])/\[Alpha] (Non/(Non + Noff))] +

> Noff*Log[(1 + \[Alpha]) (Noff/(Non + Noff))])^(

> 1/2), -Sqrt[

> 2] (Non*Log[(1 + \[Alpha])/\[Alpha] (Non/(Non + Noff))] +

> Noff*Log[(1 + \[Alpha]) (Noff/(Non + Noff))])^(1/2)];

>

> ListPlot[S2[off, \[Alpha]], PlotLabel -> "Formula 17"]

> hist2 = Histogram[S2[off, \[Alpha]], "Log", "ProbabilityDensity",

> PlotLabel -> "Formula 17 LOG"]

> hist22 = Histogram[S2[off, \[Alpha]], Automatic, "ProbabilityDensity",

> PlotLabel -> "Formula 17"]

> Show[hist22, h2]

> ProbabilityScalePlot[S2[off, \[Alpha]], "Normal",

> PlotLabel -> "Formula 17"]

>

>