Tweedie Distributions: plotting

Plotting Tweedie density and distribution functions

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

vector of values at which to evaluate and plot


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


a synonym for \(\xi\)


the mean


the dispersion


what to plot: pdf (the default) means the probability function, or cdf, the cumulative distribution function


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


For details, see dtweedie


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.


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


  • tweedie.plot
### 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)

Community examples

Looks like there are no examples yet.