# tweedie.plot

##### Tweedie Distributions: plotting

Plotting Tweedie density and distribution functions

- Keywords
- models

##### Usage

`tweedie.plot(y, xi, mu, phi, type="pdf", power=NULL, add=FALSE, ...)`

##### Arguments

- y
vector of values at which to evaluate and plot

- xi
the value of \(\xi\) such that the variance is \(\mbox{var}[Y]=\phi\mu^{\xi}\)

- power
a synonym for \(\xi\)

- mu
the mean

- phi
the dispersion

- type
what to plot:

`pdf`

(the default) means the probability function, or`cdf`

, the cumulative distribution function- add
if

`TRUE`

, the plot is added to the current device; if`FALSE`

(the default), a new plot is produced- ...
Arguments to be passed to the plotting method

##### Details

For details, see `dtweedie`

##### Value

this function is usually called for side-effect of
producing a plot of the specified Tweedie distribution,
properly plotting the exact zero that occurs at \(y=0\)
when \(1<p<2\).
However,
it also produces a list with the computed density at the given points,
with components `y`

and `x`

respectively,
such that `plot(y~x)`

approximately reproduces the plot.

##### References

Dunn, P. K. and Smyth, G. K. (2008).
Evaluation of Tweedie exponential dispersion model densities by Fourier inversion.
*Statistics and Computing*,
**18**, 73--86.
10.1007/s11222-007-9039-6

Dunn, Peter K and Smyth, Gordon K (2005).
Series evaluation of Tweedie exponential dispersion model densities
*Statistics and Computing*,
**15**(4). 267--280.
10.1007/s11222-005-4070-y

Dunn, Peter K and Smyth, Gordon K (2001).
Tweedie family densities: methods of evaluation.
*Proceedings of the 16th International Workshop on Statistical Modelling*,
Odense, Denmark, 2--6 July

Jorgensen, B. (1987).
Exponential dispersion models.
*Journal of the Royal Statistical Society*, B,
**49**, 127--162.

Jorgensen, B. (1997).
*Theory of Dispersion Models*.
Chapman and Hall, London.

Nolan, John P (1997).
Numerical calculation of stable densities and distribution functions.
*Communication in Statistics---Stochastic models*,
**13**(4). 759--774.
10.1080/15326349708807450

Sidi, Avram (1982).
The numerical evaluation of very oscillatory infinite integrals by
extrapolation.
*Mathematics of Computation*
**38**(158), 517--529.
10.1090/S0025-5718-1982-0645667-5

Sidi, Avram (1988).
A user-friendly extrapolation method for
oscillatory infinite integrals.
*Mathematics of Computation*
**51**(183), 249--266.
10.1090/S0025-5718-1988-0942153-5

Tweedie, M. C. K. (1984).
An index which distinguishes between some important exponential families.
*Statistics: Applications and New Directions.
Proceedings of the Indian Statistical Institute Golden Jubilee International Conference*
(Eds. J. K. Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical Institute.

##### See Also

##### Examples

```
# NOT RUN {
### Plot a Tweedie density with 1<p<2
yy <- seq(0,5,length=100)
tweedie.plot( power=1.7, mu=1, phi=1, y=yy, lwd=2)
tweedie.plot( power=1.2, mu=1, phi=1, y=yy, add=TRUE, lwd=2, col="red")
legend("topright",lwd=c(2,2), col=c("black","red"), pch=c(19,19),
legend=c("p=1.7","p=1.2") )
### Plot distribution functions
tweedie.plot( power=1.05, mu=1, phi=1, y=yy,
lwd=2, type="cdf", ylim=c(0,1))
tweedie.plot( power=2, mu=1, phi=1, y=yy,
add=TRUE, lwd=2, type="cdf",col="red")
legend("bottomright",lwd=c(2,2), col=c("black","red"),
legend=c("p=1.05","p=2") )
### Now, plot two densities, combining p>2 and 1<p<2
tweedie.plot( power=3.5, mu=1, phi=1, y=yy, lwd=2)
tweedie.plot( power=1.5, mu=1, phi=1, y=yy, lwd=2, col="red", add=TRUE)
legend("topright",lwd=c(2,2), col=c("black","red"), pch=c(NA,19),
legend=c("p=3.5","p=1.5") )
# }
```

*Documentation reproduced from package tweedie, version 2.3.2, License: GPL (>= 2)*