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MathGroup Archive 2012

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Erf funcion

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123947] Erf funcion
  • From: Vicent <vginer at gmail.com>
  • Date: Sun, 1 Jan 2012 02:29:27 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello.

I have an expression that depends on the Cumulative Distribution
Function (CDF) of a Normal Variable with mean = 0 and standard
deviation = 1.

When I perform operations and/or derivatives with/for that function
with Mathematica, I get expressions involving Erf function, as the CDF
function of a Normal distributed variable and Erf (error function) are
closely related. Concretely,

    FiX[x] == (1/2)*(1 + Erf[x/Sqrt[2]])

and thus

    Erf[x] == 2*FiX[x*Sqrt[2]] - 1

where FiX stands for the previously mentioned CDF, I mean:

    X = NormalDistribution[0, 1]
    FiX[x_] := CDF[X, x]


Is there a quick way to ask Mathematica not to use  Erf  but always
let the results as a function of FI[x]??

The expressions I get as a result of my computations are larger than
this short example:

    3 (2^(7/2 - 2 (k + t))) Cp (  E^(-d^2 - (36 Cp^2)/lambda^2))
((Erf[(-d + (6 Cp)/lambda)/Sqrt[2]] + Erf[(6 Cp + d lambda)/(Sqrt[2]
lambda)])^k)

where "Cp", "k", "t", "d" and "lambda" are parameters or arguments
that I want to keep as "generic".

So, how can I "translate" expressions such as the last one into "FiX
mode"? Or, better, how can I prevent Mathematica to reduce everything
to "Erf mode"??

I hope my question is clear enough... :)

Thank you very much in advance for your answers.

And have a good new year!


--
vicent
dooid.com/vicent



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