inc.beta.deriv {curesurv} | R Documentation |
computes the first and second derivatives of incomplete Beta
function with respect of Beta parameters p and or q using algorithm
differentiating the aproximants of I_{x,p,q}
formula in terms of forward
recurrence relations where the the n^{th}
approximant can be expressed as :
I_{x,p,q} \approx K_{x,p,q} A_n/B_n
, n \geq 1
This technique was proposed by Moore (1982) to calculate the derivatives of incomplete gamma function.
inc.beta.deriv(
x,
p = stop("p must be specified"),
q = stop("q must be specified"),
err = .Machine$double.eps * 10000,
minapp = 2,
maxapp = 1000
)
x |
vector of length k containing values to which the beta function is to be integrated |
p |
Beta shape1 parameter |
q |
Beta shape2 parameter. shape1 and shape2 can be vertors in the same dimension as x or scalars |
err |
value for error |
minapp |
minimal bound value |
maxapp |
external noud value |
An object of class FD.inc.beta
.
This object is a list containing 15 components. The first 13 components in
the list are each a vector of the same length as x (u in the model). The two
last elements are scalar terms. The output elements are:
I |
|
Ip |
|
Ipp |
|
Iq |
|
Iqq |
|
Ipq |
|
log.Beta |
|
digamma.p |
|
trigamma.p |
|
digamma.q |
|
trigamma.q |
|
digamma.pq |
|
trigamma.pq |
|
nappx |
highest order approximant evaluated. Iteration stops if nappx>maxappx |
errapx |
approximate maximum absolute error of computed derivatives |
Boik, Robert J., and James F. Robison-Cox. "Derivatives of the incomplete beta function." Journal of Statistical Software 3.1 (1998): 1-20. (arXiv)