dtweedie.saddle(y, power, mu, phi, eps=1/6)
eps=1/6
(as suggested by Nelder and Pregibon, 1987).mu
,
phi
and
power
.power
,
the distributions are still defined but cannot be written in closed form,
and hence evaluation is very difficult.
When $12$, the distributions are continuous for $Y$ greater than zero.
This function approximates the density using the saddlepoint approximation defined by Nelder and Pregibon (1987).
Daniels, H. E. (1980). Exact saddlepoint approximations. Biometrika, 67, 59--63.
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.
Nelder, J. A. and Pregibon, D. (1987). An extended quasi-likelihood function. Biometrika, 74(2), 221--232.
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.
dtweedie
p <- 2.5
mu <- 1
phi <- 1
y <- seq(0, 10, length=100)
fy <- dtweedie( y=y, power=p, mu=mu, phi=phi)
plot(y, fy, type="l")
# Compare to the saddlepoint density
f.saddle <- dtweedie.saddle( y=y, power=p, mu=mu, phi=phi)
lines( y, f.saddle, col=2 )
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