mgcv (version 1.9-0)

rig: Generate inverse Gaussian random deviates

Description

Generates inverse Gaussian random deviates.

Usage

rig(n,mean,scale)

Value

A vector of inverse Gaussian random deviates.

Arguments

n

the number of deviates required. If this has length > 1 then the length is taken as the number of deviates required.

mean

vector of mean values.

scale

vector of scale parameter values (lambda, see below)

Author

Simon N. Wood

Details

If x if the returned vector, then E(x) = mean while var(x) = scale*mean^3. For density and distribution functions see the statmod package. The algorithm used is Algorithm 5.7 of Gentle (2003), based on Michael et al. (1976). Note that scale here is the scale parameter in the GLM sense, which is the reciprocal of the usual `lambda' parameter.

References

Gentle, J.E. (2003) Random Number Generation and Monte Carlo Methods (2nd ed.) Springer.

Michael, J.R., W.R. Schucany & R.W. Hass (1976) Generating random variates using transformations with multiple roots. The American Statistician 30, 88-90.

https://www.maths.ed.ac.uk/~swood34/

Examples

require(mgcv)
set.seed(7)
## An inverse.gaussian GAM example, by modify `gamSim' output... 
dat <- gamSim(1,n=400,dist="normal",scale=1)
dat$f <- dat$f/4 ## true linear predictor 
Ey <- exp(dat$f);scale <- .5 ## mean and GLM scale parameter
## simulate inverse Gaussian response...
dat$y <- rig(Ey,mean=Ey,scale=.2)
big <- gam(y~ s(x0)+ s(x1)+s(x2)+s(x3),family=inverse.gaussian(link=log),
          data=dat,method="REML")
plot(big,pages=1)
gam.check(big)
summary(big)