OwenT {dsfa} | R Documentation |
Evaluates the Owen T-function
OwenT(x, a, jmax = 50, cut.point = 8, deriv = 0)
OwenT_vec(x, a, jmax = 50, cut.point = 8)
x |
numeric vector of quantiles. Missing values (NAs) and Inf are allowed. |
a |
numeric vector. Inf is allowed. |
jmax |
an integer scalar value which regulates the accuracy of the result. |
cut.point |
a scalar value which regulates the behaviour of the algorithm. |
deriv |
derivative of order |
The OwenT function is defined as
T(x,a)=\frac{1}{2 \pi} \int_0^{a} \frac{\exp\{-x^2 (1+t^2)/2 \}}{1+t^2} d t
. If a
>1 and 0<x
<=cut.point
, a series expansion is used, truncated after jmax
terms. If a
>1 and x
>cut.point
,
an asymptotic approximation is used. In the other cases, various reflection properties of the function are exploited. For deriv
=0, the function is a clone of T.Owen
.
OwenT
evaluates the OwenT function with given parameters x
and a
. If the derivatives are calculated these are provided as the attributes gradient
, hessian
.
OwenT_vec()
: Vectorized OwenT function without derivatives.
Owen DB (1956). “Tables for Computing Bivariate Normal Probabilities.” Annals of Mathematical Statistics, 27, 1075-1090.
OwenT(x=1, a=1, jmax = 50, cut.point = 8, deriv=2)