invnorm: The inverse normal distribution

In nisone: Inference for Samples of Size at Least One

The inverse normal distribution

Description

Density, distribution function, quantile function, and random generation for the inverse normal distribution when parameterized by the mean and standard deviation of the inverse (reciprocal).

Usage

dinvnorm(x, imean = 0, isd = 1, log = FALSE)

pinvnorm(q, imean = 0, isd = 1, lower.tail = TRUE, log.p = FALSE)

qinvnorm(p, imean = 0, isd = 1)

rinvnorm(n, imean = 0, isd = 1)

Arguments

x, q	vector of quantiles
imean	vector of means of inverse.
isd	vector of standard deviations of inverse.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P(X<=x) otherwise, P(X>x).
p	vector of probabilities
n	sample size

Value

Either a random sample (rinvnorm), the density (dinvnorm), the tail probability (pinvnorm), or the quantile (qinvnorm) of the inverse normal distribution.

Functions

• dinvnorm(): Density function.

• pinvnorm(): Probability function.

• qinvnorm(): Quantile function.

• rinvnorm(): Random generation.

Author(s)

David Gerard

References

• Robert, C. (1991). Generalized inverse normal distributions. Statistics & Probability Letters, 11(1), 37-41. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/0167-7152(91)90174-P")}

Examples

x <- seq(-4, 4, length.out = 300)
y <- dinvnorm(x = x, imean = 0.1, isd = 1)
graphics::plot(x, y, type = "l")

p <- pinvnorm(q = x, imean = 0.1, isd = 1)
graphics::plot(x, p, type = "l", ylim = c(0, 1))
graphics::abline(h = c(0, 1), lty = 2)

qinvnorm(p = c(0.025, 0.5, 0.975), imean = 0.1, isd = 1)

s <- rinvnorm(n = 10000, imean = 0.1, isd = 1)
stats::quantile(s, c(0.025, 0.5, 0.975))

nisone documentation built on Sept. 8, 2026, 5:08 p.m.