rTweedie {mgcv} R Documentation

## Generate Tweedie random deviates

### Description

Generates Tweedie random deviates, for powers between 1 and 2.

### Usage

```rTweedie(mu,p=1.5,phi=1)
```

### Arguments

 `mu` vector of expected values for the deviates to be generated. One deviate generated for each element of `mu`. `p` the variance of a deviate is proportional to its mean, `mu` to the power `p`. `p` must be between 1 and 2. 1 is Poisson like (exactly Poisson if `phi=1`), 2 is gamma. `phi` The scale parameter. Variance of the deviates is given by is `phi*mu^p`.

### Details

A Tweedie random variable with 1<p<2 is a sum of `N` gamma random variables where `N` has a Poisson distribution, with mean `mu^(2-p)/((2-p)*phi)`. The Gamma random variables that are summed have shape parameter `(2-p)/(p-1)` and scale parameter `phi*(p-1)*mu^(p-1)` (note that this scale parameter is different from the scale parameter for a GLM with Gamma errors).

This is a restricted, but faster, version of `rtweedie` from the `tweedie` package.

### Value

A vector of random deviates from a Tweedie distribution, expected value vector `mu`, variance vector `phi*mu^p`.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### References

Peter K Dunn (2009). tweedie: Tweedie exponential family models. R package version 2.0.2. https://cran.r-project.org/package=tweedie

`ldTweedie`, `Tweedie`

### Examples

``` library(mgcv)
f2 <- function(x) 0.2 * x^11 * (10 * (1 - x))^6 + 10 *
(10 * x)^3 * (1 - x)^10
n <- 300
x <- runif(n)
mu <- exp(f2(x)/3+.1);x <- x*10 - 4
y <- rTweedie(mu,p=1.5,phi=1.3)
b <- gam(y~s(x,k=20),family=Tweedie(p=1.5))
b
plot(b)

```

[Package mgcv version 1.8-31 Index]