OwensT: Owen's T-function

In PowerTOST: Power and Sample Size for (Bio)Equivalence Studies

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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

PowerTOST documentation built on May 29, 2024, 4:40 a.m.