Tweedie Distributions: plotting

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Description

Plotting Tweedie density and distribution functions

Usage

1
   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 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.

Author(s)

Peter Dunn (pdunn2@usc.edu.au)

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.

Dunn, Peter K and Smyth, Gordon K (2005). Series evaluation of Tweedie exponential dispersion model densities Statistics and Computing, 15(4). 267–280.

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.

Sidi, Avram (1982). The numerical evaluation of very oscillatory infinite integrals by extrapolation. Mathematics of Computation 38(158), 517–529.

Sidi, Avram (1988). A user-friendly extrapolation method for oscillatory infinite integrals. Mathematics of Computation 51(183), 249–266.

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

dtweedie

Examples

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### 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") )