PowerTOST (version 1.4-7)

OwensT: Owen's T-function

Description

Calculates the definite integral from 0 to a of exp(-0.5*h^2*(1+x^2))/(1+x^2)/(2*pi).

Usage

OwensT(h, a)

Arguments

h

parameter h

a

upper limit of integration

Value

Numerical value of the definite integral.

Details

The function is an R port of FORTRAN code given in the references and MATLAB code given on http://people.sc.fsu.edu/~jburkardt/m_src/asa076/asa076.html by John Burkardt under the GNU LGPL license. The arguments of OwensT() have to be scalars because the implementation doesn't vectorize.

References

Goedhart PW, Jansen MJW. Remark AS R89: A Remark on Algorithm AS 76: An Integral Useful in Calculating Central t and Bivariate Normal Probabilities J Royal Stat Soc C. 1992;41(2):496--7. 10.2307/2347586

Boys R. Algorithm AS R80: A Remark on Algorithm AS 76: An Integral Useful in Calculating Noncentral t and Bivariate Normal Probabilities J Royal Stat Soc C. 1989;38(3):580--2. 10.2307/2347755

Thomas GE. Remark ASR 65: A Remark on Algorithm AS76: An Integral Useful in Calculating Non-Central t and Bivariate Normal Probabilities J Royal Stat Soc C. 1986;35(3):310--2. 10.2307/2348031

Chou Y-M. Remark AS R55: A Remark on Algorithm AS 76: An Integral Useful in Calculating Noncentral T and Bivariate Normal Probabilities J Royal Stat Soc C. 1985;34(1):100--1. 10.2307/2347894

Thomas GE. Remark AS R30: A Remark on Algorithm AS 76: An Integral Useful in Calculating Non-Central t and Bivariate Normal Probabilities J Royal Stat Soc C. 1979;28(1):113. 10.2307/2346833

Young JC, Minder C. Algorithm AS 76: An Integral Useful in Calculating Non-Central t and Bivariate Normal Probabilities J Royal Stat Soc C. 1974;23(3):455--7. 10.2307/2347148

Owen DB. Tables for Computing Bivariate Normal Probabilities Ann Math Stat. 1956;27(4):1075--90. 10.1214/aoms/1177728074

See Also

OwensQOwen, OwensQ

Examples

# NOT RUN {
OwensT(2.5, 0.75)
# should give [1]  0.002986697
# value from Owen's tables is 0.002987
OwensT(2.5, -0.75)
# should give [1] -0.002986697
# }