Tweedie Distributions: plotting
Plotting Tweedie density and distribution functions
tweedie.plot(y, xi, mu, phi, type="pdf", power=NULL, add=FALSE, ...)
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: |
add |
if |
... |
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.
Peter Dunn (pdunn2@usc.edu.au)
Dunn, P. K. and Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing, 18, 73–86. 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. 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. doi: 10.1080/15326349708807450
Sidi, Avram (1982). The numerical evaluation of very oscillatory infinite integrals by extrapolation. Mathematics of Computation 38(158), 517–529. 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. 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.
### 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") )Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.