OwensT {PowerTOST}

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

Details

The function is an R port of FORTRAN code given in the references and MATLAB code given by John Burkardt under the GNU LGPL license.

The arguments of OwensT() have to be scalars because the implementation doesn’t vectorize.

Value

Numerical value of the definite integral.

Note

This function is only needed as auxiliary in OwensQOwen.
But may be useful for others.

Author(s)

MATLAB code by J. Burkardt, R port by D. Labes

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. doi: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. doi: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. doi: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. doi: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. doi: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. doi:10.2307/2347148

Burkardt J. ASA076. Owen's T Function. https://people.math.sc.edu/Burkardt/f_src/asa076/asa076.html

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

See Also

OwensQOwen, OwensQ

Examples

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