My random variable of interest is the ratio of a Gaussian normal distributed variable and a Richardson self similar distribution. These two variables are independent.
Is it possible to get an analytical formula of the ratio distribution associated with these two random variables? (I have put in attach there the expression of both variables). Thanks!
Hi
It is quite simple to do this integral using Mathematica - here's the output
1/(25515πz^6 ) 64b^(9⁄2) (4b^(3⁄2) π(-12zBesselJ[-1/3,(2√(2/3) b^(3⁄2))/3z]+15zBesselJ[1/3,(2√(2/3) b^(3⁄2))/3z]+√6 b^(3⁄2) (BesselJ[2/3,(2√(2/3) b^(3⁄2))/3z]-BesselJ[4/3,(2√(2/3) b^(3⁄2))/3z]))+81√2 z^2 HypergeometricPFQ[{2},{1/3,2/3},-(2b^3)/(27z^2 )])
In case it is still not clear, BesselJ - is the Bessel function of the first kind, known as J
and the HypergeometricPFQ , is actually the 1F2 hypergeometric function
you can read about these functions in wikipedia/Mathworld
http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html
http://functions.wolfram.com/HypergeometricFunctions/HypergeometricPFQ/
- Badges
- Science topic