Compute Owen's T Function T(h, a)

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)

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.

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.

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).

See also

pnorm, dnorm

Examples

if (FALSE) { # \dontrun{
  # Basic usage. Vectorized 'a'
  h <- c(-1, 0, 1, 2)
  a <- 0.5
  TOwen(h, a)

  # Vectorized 'a' with non-finite entries; non-finite entries yield NA
  a2 <- c(0.2, NA, 1, Inf)
  TOwen(h, a2)
} # }