[R] Modified Bessel Function - 2nd kind
Dr Andrew Wilson
eia018 at comp.lancs.ac.uk
Wed Dec 11 13:59:06 CET 2002
Many thanks for this pointer.
Using the formula from the page you referenced, I now have the formula
with the modified Bessel function of the second kind:
> x <- c(1,2,3,4,5,6,7,8)
> y <- c(1,4,5,7,5,4,1,1)
> library(nls)
> library(gregmisc)
> y2 <- nls(y ~
sqrt((2*a)/pi)*exp(a*sqrt(1-q))*((((a*q)/2)^x)/factorial(x))* ((pi/2) *
(besselI(a,-(x-0.5)) - besselI(a,(x-0.5)))/sin((x-0.5) * pi)),
start=list(a=0.1,q=0.1),trace=TRUE)
However, for some reason, I get the following error message:
133.9999 : 0.100 0.001
Error in numericDeriv(form[[3]], names(ind), env) :
Missing value or an Infinity produced when evaluating the model
In addition: Warning messages:
1: NaNs produced in: sqrt((2 * a)/pi)
2: NaNs produced in: sqrt(1 - q)
3: NaNs produced in: besselI(x, nu, 1 + as.logical(expon.scaled))
4: NaNs produced in: besselI(x, nu, 1 + as.logical(expon.scaled))
Could anyone tell me what I'm doing wrong (and how to fix it)?
The following constraints should apply to the parameters, but I'm not
aware of a "constrain" option in nls that allows me to set these minima
and maxima:
0 < q < 1
a > 0
Many thanks,
Andrew Wilson
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