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.

```
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)
```

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.

- 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

Mikis Stasinopoulos, Bob Rigby and Nicoleta Motpan

The specific parameterization of the exponential distribution used in EXP is $$f(y|\mu)=\frac{1}{\mu} \exp\left\{-\frac{y}{\mu}\right\}$$ for y>0, \(\mu>0\) see pp. 422-23 of Rigby et al. (2019).

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,tools:::Rd_expr_doi("10.1201/9780429298547"). 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, tools:::Rd_expr_doi("10.18637/jss.v023.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.
tools:::Rd_expr_doi("10.1201/b21973")

(see also https://www.gamlss.com/).

`gamlss.family`

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

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