R: Inverse Gaussian distribution for fitting a GAMLSS

IG {gamlss.dist} | R Documentation

## Inverse Gaussian distribution for fitting a GAMLSS

### Description

The function `IG()`, or equivalently `Inverse.Gaussian()`, defines the inverse Gaussian distribution, a two parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The functions `dIG`, `pIG`, `qIG` and `rIG` define the density, distribution function, quantile function and random generation for the specific parameterization of the Inverse Gaussian distribution defined by function `IG`.

### Usage

    IG(mu.link = "log", sigma.link = "log")
    dIG(x, mu = 1, sigma = 1, log = FALSE)
    pIG(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
    qIG(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
    rIG(n, mu = 1, sigma = 1, ...)

### Arguments

`mu.link` | Defines the `mu.link`, with "log" link as the default for the mu parameter
`sigma.link` | Defines the `sigma.link`, with "log" link as the default for the sigma parameter
`x,q` | vector of quantiles
`mu` | vector of location parameter values
`sigma` | vector of scale parameter values
`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` | number of observations. If `length(n) > 1`, the length is taken to be the number required
`...` | `...` can be used to pass the uppr.limit argument to `qIG`

### Details

Definition file for inverse Gaussian distribution.

f(y|mu,sigma)=(1/(sqrt(2*pi*sigma^2*y^3))* exp(-(y-mu)^2/(2*mu^2*sigma^2*y))

for y>0, μ>0 and σ>0.

### Value

returns a `gamlss.family` object which can be used to fit a inverse Gaussian distribution in the `gamlss()` function.

### Note

mu is the mean and (sigma^2)*(mu^3) is the variance of the inverse Gaussian

### Author(s)

Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou

### References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

### See Also

`gamlss.family` , `GA`, `GIG`

### Examples

    IG()# gives information about the default links for the normal distribution
    # library(gamlss)
    # data(rent)
    # gamlss(R~cs(Fl),family=IG, data=rent) #
    plot(function(x)dIG(x, mu=1,sigma=.5), 0.01, 6,
     main = "{Inverse Gaussian  density mu=1,sigma=0.5}")
    plot(function(x)pIG(x, mu=1,sigma=.5), 0.01, 6,
     main = "{Inverse Gaussian  cdf mu=1,sigma=0.5}")

[Package gamlss.dist version 5.3-2 Index]