ginvnorm: The generalized inverse normal distribution

In nisone: Inference for Samples of Size at Least One

The generalized inverse normal distribution

Description

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

Usage

dginvnorm(x, alpha, mu = 0, tau = 1, log = FALSE)

pginvnorm(q, alpha, mu = 0, tau = 1, lower.tail = TRUE, subdivisions = 500L)

qginvnorm(p, alpha, mu = 0, tau = 1)

rginvnorm(n, alpha, mu = 0, tau = 1)

mginvnorm(alpha, mu = 0, tau = 1)

xginvnorm(alpha, mu = 0, tau = 1)

Arguments

x, q	vector of quantiles
alpha	vector of shape parameters
mu	vector of means of inverse.
tau	vector of standard deviations of inverse.
log	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).
subdivisions	The maximum number of subintervals used in integrate().
p	vector of probabilities
n	sample size

Value

Either a random sample (rginvnorm), the density (dginvnorm), the tail probability (pginvnorm), or the quantile (qginvnorm) of the inverse normal distribution.

Functions

• dginvnorm(): Density function.

• pginvnorm(): Probability function.

• qginvnorm(): Quantile function.

• rginvnorm(): Random generation.

• mginvnorm(): Mean.

• xginvnorm(): Modes.

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

set.seed(50)
samp <- rginvnorm(n = 1000, alpha = 4, mu = 0.5, tau = 1)
x <- seq(min(samp), max(samp), length.out = 500)
y <- dginvnorm(x = x, alpha = 4, mu = 0.5, tau = 1)
modes <- xginvnorm(alpha = 4, mu = 0.5, tau = 1)
graphics::hist(
  samp,
  freq = FALSE,
  breaks = 100,
  xlab = "x",
  main = "Generalized Inverse Normal Density")
graphics::lines(x, y, col = "#E69F00")
graphics::abline(v = modes, col = "#56B4E9", lty = 2)

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