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Sjoerd C. de Vries
Sjoerd C. de Vries
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Deriving a Rayleigh distribution in Mathematica

When I trytried to exploitfind this Rayleigh distribution Mathematica couldn't come with an answer.:

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]

I Wanna Drivewant to derive the Distribution of Rayleigh distribution in parametric form. Mathematica could Solvesolve this for N~[0,1] and the answer is Rayleigh[1], but for N~[0,k] it has no Answer!!!answer.

Rayleigh distribution in Mathematica

When I try to exploit this Rayleigh distribution Mathematica couldn't answer.

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]

I Wanna Drive the Distribution of Rayleigh in parametric form Mathematica could Solve this for N~[0,1] and the answer is Rayleigh[1] but for N~[0,k] has no Answer!!!

Deriving a Rayleigh distribution

When I tried to find this Rayleigh distribution Mathematica couldn't come with an answer:

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]

I want to derive the Rayleigh distribution in parametric form. Mathematica could solve this for N~[0,1] and the answer is Rayleigh[1], but for N~[0,k] it has no answer.

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Hamid reza
Hamid reza
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When I try to exploit this Rayleigh distribution Mathematica couldn't answer.

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]

I Wanna Drive the Distribution of Rayleigh in parametric form Mathematica could Solve this for N~[0,1] and the answer is Rayleigh[1] but for N~[0,k] has no Answer!!!

When I try to exploit this Rayleigh distribution Mathematica couldn't answer.

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]

When I try to exploit this Rayleigh distribution Mathematica couldn't answer.

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]

I Wanna Drive the Distribution of Rayleigh in parametric form Mathematica could Solve this for N~[0,1] and the answer is Rayleigh[1] but for N~[0,k] has no Answer!!!

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edit approved Apr 11, 2015 at 15:34
m0nhawk
edit approved Apr 11, 2015 at 15:34
m0nhawk
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Rayleigh distribution in Mathematica couldn't Solve this.Why?

when iWhen I try to Exploitexploit this rayleigh Distribution mathematicaRayleigh distribution Mathematica couldn't answer!!.

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[\[Mu]1NormalDistribution[μ1, \[Sigma]]σ], 
   x2 \[Distributed] NormalDistribution[\[Mu]2NormalDistribution[μ2, \[Sigma]]σ]}, 
  Assumptions -> \[Mu]1μ1 == \[Mu]2μ2 == 0], r]

Mathematica couldn't Solve this.Why?

when i try to Exploit this rayleigh Distribution mathematica couldn't answer!!

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[\[Mu]1, \[Sigma]], 
   x2 \[Distributed] NormalDistribution[\[Mu]2, \[Sigma]]}, 
  Assumptions -> \[Mu]1 == \[Mu]2 == 0], r]

Rayleigh distribution in Mathematica

When I try to exploit this Rayleigh distribution Mathematica couldn't answer.

PDF[TransformedDistribution[
  Sqrt[x1^2 + x2^2], {x1 \[Distributed] 
    NormalDistribution[μ1, σ], 
   x2 \[Distributed] NormalDistribution[μ2, σ]}, 
  Assumptions -> μ1 == μ2 == 0], r]
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Hamid reza
Hamid reza
  • 43
  • 5