dtweedie_saddle: Tweedie densities evaluation using the saddlepoint...

In tweedie: Evaluation of Tweedie Exponential Family Models

Tweedie densities evaluation using the saddlepoint approximation

Description

Density function for the Tweedie EMDs using a saddlepoint approximation.

Usage

dtweedie_saddle(y, xi = NULL, mu, phi, eps = 1/6, power = NULL)

dtweedie.saddle(y, xi = NULL, mu, phi, eps = 1/6, power = NULL)

Arguments

y	vector of quantiles.
xi	scalar; the value of \xi such that the variance is \mbox{var}[Y]=\phi\mu^{\xi}. A synonym for power.
mu	vector of mean \mu.
phi	vector of dispersion parameters \phi.
eps	the offset in computing the variance function; the default is eps=1/6 (as suggested by Nelder and Pregibon, 1987).
power	scalar; a synonym for \xi, the Tweedie index parameter.

Value

A numeric vector of densities.

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11222-005-4070-y")}

Nelder, J. A. and Pregibon, D. (1987). An extended quasi-likelihood function Biometrika, 74(2), 221–232. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/74.2.221")}

Examples

# Plot a Tweedie density
y <- seq(0.01, 4, length = 50)
fy <- dtweedie_saddle(y, power = 1.1, mu = 1, phi = 1)
plot(y, fy, type = "l", lwd = 2, ylab = "Density")

tweedie documentation built on Feb. 7, 2026, 5:07 p.m.