EXP: 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)

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.

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

Author

Mikis Stasinopoulos, Bob Rigby and Nicoleta Motpan

Details

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).

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,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/).

Examples

Run this code

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

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