Mills Ratio Functions for Various Distributions — mills_ratio

Functions to compute Mills ratios for different probability distributions. The Mills ratio m(x) is defined as the ratio of the complementary cumulative distribution function (CCDF) to the probability density function (PDF): m(x) = \[1 - F(x)\] / f(x)

Usage

mills_ratio_normal(x, mean = 0, sd = 1, log = FALSE)

Arguments

x: Numeric vector of quantiles
mean: Mean of the distribution (default = 0)
sd: Standard deviation (default = 1)
log: Logical; if TRUE, returns log(Mills ratio) for numerical stability

Value

Numeric vector of Mills ratios

Author

John Gavin john.b.gavin@gmail.com Compute Mills Ratio for Normal Distribution

Examples

# Standard normal Mills ratio at x = 2
mills_ratio_normal(2)
#> [1] 0.4213692

# Multiple values
mills_ratio_normal(c(1, 2, 3, 4))
#> [1] 0.6556795 0.4213692 0.3045903 0.2366524

# Log Mills ratio for extreme values
mills_ratio_normal(10, log = TRUE)
#> [1] -2.312347