tweedie (version 2.3.3)

tweedie.plot: Tweedie Distributions: plotting

Description

Plotting Tweedie density and distribution functions

Usage

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

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.

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

Author

Peter Dunn (pdunn2@usc.edu.au)

Details

For details, see dtweedie

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. tools:::Rd_expr_doi("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. tools:::Rd_expr_doi("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. tools:::Rd_expr_doi("10.1080/15326349708807450")

Sidi, Avram (1982). The numerical evaluation of very oscillatory infinite integrals by extrapolation. Mathematics of Computation 38(158), 517--529. tools:::Rd_expr_doi("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. tools:::Rd_expr_doi("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

dtweedie

Examples

Run this code
### 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") )

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