p.s.  Orthogonal polynomials can be defined for any probability 
distribution on the real line, discrete, continuous, or otherwise, as 
described in the Wikipedia article on "orthogonal polynomials".


On 10/10/2013 5:02 PM, Marino David wrote:
> Hi all,
>
> We know that Hermite polynomial is for
> Gaussian, Laguerre polynomial for Exponential
> distribution, Legendre polynomial for uniform
> distribution, Jacobi polynomial for Beta distribution. Does anyone know
> which kind of polynomial deals with the log-normal,


       * lognormal in X is normal for Z = log(X).  Therefore, you'd use 
Hermite polynomials in Z.


> Student's t, Inverse
> gamma and Fisher's F distribution?


       * If X follows an F(d1, d2) distribution, then Z = d1*x/(x1*x+d2) 
follows a beta distribution.  Use Jacobi polynomials on Z.


       * If X follows a student's t(df), then X^2 follows an F(1, df) 
distribution.  Again, use Jacobi on the appropriate transform.


       * If X follows an inverse gamma, then 1/X follows a gamma 
distribution.


       Does this answer the question?


       Spencer
> Thank you in advance!
>
> David
>
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>
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