[R-SIG-Finance] bessel functions

[stefano iacus]

On 16/set/06, at 00:00, Martin Maechler wrote:

> Hi Stefano,  et al.
>
> I have been too busy to get this earlier,
>
>>>>>> "Stefano" == stefano iacus <stefano.iacus at unimi.it>
>>>>>>     on Thu, 14 Sep 2006 19:28:15 +0900 writes:
>
>     Stefano> Hi, does anyone know about a reliable algorithm to
>     Stefano> evaluate the exponentially rescaled bessel function
>     Stefano> of first find, any order, real argument?
>
>     Stefano> what I need is the equivalent of R function
>
>     Stefano> besselI(x, nu, expon.scaled = TRUE)
>
>     Stefano> for large real x (say 5000) and large nu (say 10 to
>     Stefano> 30)
>
>     Stefano> The R implementation does not satisfy my needs
>     Stefano> because, for example,
>
>
>>> besselI(5539.947191,11,exp=TRUE)
>     Stefano> [1] NaN
>
>     Stefano> but if you ask Mathematica you get this number:
>     Stefano> 0.00530180603357
>
>     Stefano> To be more specific I need this to evaluate the
>     Stefano> likelihood of the CIR model. I know there are many
>     Stefano> different estimators for the CIR but I need to
>     Stefano> evaluate the likelihood.
>
>     Stefano> Googling around did not help me.
>
> But  RSiteSearch("bessel")  does immediately help
>
> The answer is *not* to use numerical recipes
> (they have ``source'' but have heavily restricted copyrights;
>  and also very often, their code is far suboptimal) as 'mel'
> indicated, but  for "special math functions" like these,
> rather look at the GSL = GNU Scientific Library.

I agree, numerical recipies is not the solution. Thanks for pointing  
me to gsl !!!

stefano

>
> It has all kinds of Bessel functions and uses newer versions of
> the algorithm than R, since
> --- as we have the 'gsl' package on CRAN - thanks to Robin Hankin ---
> you get the desired result from
>
>> library(gsl)
>> bessel_In_scaled(x= 5539.947191, n= 11)
>  [1] 0.005301806
>
>
> Martin Maechler