TOwen1 computes an Owen's \(T\)-function variant (or a related
special function) for vectors h and a based on the t function in https://people.sc.fsu.edu/~jburkardt/c_src/owen/owen.html. Non-finite inputs (in h or a) produce NA
at corresponding positions, while finite pairs are computed in C in a
vectorized fashion.
Usage
TOwen(h, a, threads = 1)
Value
A numeric vector of length length(h) containing \(T(h_i, a_i)\).
Elements where either h_i or a_i is not finite are NA.
The returned object is given class "snreg" for downstream compatibility
with your package’s print/summary helpers.
Arguments
h
numeric vector of \(h\) arguments.
a
numeric vector of \(a\) arguments. Must be either the same length as h
or of length 1 (will be recycled by standard R rules).
threads
integer. Number of threads to request from the C implementation (if supported).
Default is 1.
Details
Owen's T Function via C Backend
Owen's \(T\) function is commonly defined as
$$T(h, a) \;=\; \frac{1}{2\pi} \int_{0}^{a} \frac{\exp\!\left(-\tfrac{1}{2}h^2 (1+t^2)\right)}{1+t^2} \, dt,$$
for real \(h\) and \(a\).
The function accepts vector inputs and:
Computes results only for entries where both h and a are finite.
Returns NA where either h or a is non-finite.
Optionally passes a threads hint to the C backend (ignored if not supported).