R: Exponential distribution for fitting a GAMLSS

EXP {gamlss.dist} | R Documentation

## Exponential distribution for fitting a GAMLSS

### Description

The function EXP defines the exponential distribution, a one parameter distribution for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`. The `mu` parameter represents the mean of the distribution. The functions `dEXP`, `pEXP`, `qEXP` and `rEXP` define the density, distribution function, quantile function and random generation for the specific parameterization of the exponential distribution defined by function EXP.

### Usage

    EXP(mu.link ="log")
    dEXP(x, mu = 1, log = FALSE)
    pEXP(q, mu = 1, lower.tail = TRUE, log.p = FALSE)
    qEXP(p, mu = 1, lower.tail = TRUE, log.p = FALSE)
    rEXP(n, mu = 1)

### Arguments

`mu.link` | Defines the mu.link, with "log" link as the default for the `mu` parameter, other links are "inverse" and "identity"
`x,q` | vector of quantiles
`mu` | vector of location 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

### Details

The specific parameterization of the exponential distribution used in EXP is

f(y|mu)=1/mu*exp(-y/mu)

, for y>0, mu>0.

### Value

EXP() returns a gamlss.family object which can be used to fit an exponential distribution in the gamlss() function. dEXP() gives the density, pEXP() gives the distribution function, qEXP() gives the quantile function, and rEXP() generates random deviates.

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby and Nicoleta Motpan

### 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.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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, http://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`

### Examples

    y<-rEXP(1000,mu=1) # generates 1000 random observations
    hist(y)
    # library(gamlss)
    # histDist(y, family=EXP)

[Package gamlss.dist version 5.0-2 Index]