new.dist (version 0.1.1)

uigd: Unit Inverse Gaussian Distribution

Description

Density, distribution function, quantile function and random generation for the Unit Inverse Gaussian distribution mean and scale.

Usage

duigd(x, mu, lambda = 1, log = FALSE)
puigd(q, mu, lambda = 1, lower.tail = TRUE, log.p = FALSE)
quigd(p, mu, lambda = 1, lower.tail = TRUE)
ruigd(n, mu, lambda = 1)

Value

duigd gives the density, puigd gives the distribution function, quigd gives the quantile function and ruigd generates random deviates.

Arguments

x, q

vector of quantiles.

mu

a mean parameter.

lambda

a scale parameter.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P\left[ X\leq x\right]\), otherwise, \(P\left[ X>x\right] \).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Unit Inverse Gaussian distribution scale parameter \(\lambda\) and mean parameter \(\mu\), has density $$f\left( x\right) =\sqrt{\frac{\lambda }{2\pi }} \frac{1}{x^{3/2}}e^{-\frac{ \lambda }{2\mu ^{2}x}\left( x-\mu \right) ^{2}},$$ where $$x>0,~\mu ,\lambda >0.$$

References

Ghitany, M., Mazucheli, J., Menezes, A. ve Alqallaf, F., 2019, The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval, Communications in Statistics-Theory and Methods, 48 (14), 3423-3438.

Examples

library(new.dist)
duigd(1, mu=2, lambda=3)
puigd(1,mu=2,lambda=3)
quigd(.1,mu=2,lambda=3)
ruigd(10,mu=2,lambda=3)