uigd {new.dist}

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)

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.

Value

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

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)