Mills Ratio

Computes the Mills ratio.

Usage

mills.ratio(x)
mills.ratio2(x)

Arguments

x

Numeric (real).

Details

The Mills ratio here is dnorm(x) / pnorm(x) (some use (1 - pnorm(x)) / dnorm(x)). Some care is needed as x approaches -Inf; when \(x\) is very negative then its value approaches \(-x\).

Value

mills.ratio returns the Mills ratio, and mills.ratio2 returns dnorm(x) * dnorm(x) / pnorm(x).

References

Mills, J. P. (1926). Table of the ratio: area to bounding ordinate, for any portion of normal curve. Biometrika. 18(3/4), 395–400.

Author

T. W. Yee

Examples

if (FALSE) { # \dontrun{
curve(mills.ratio, -5, 5, col = "orange", las = 1)
curve(mills.ratio, -5, 5, col = "orange", las = 1, log = "y")
} # }