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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