dtweedie_inversion: Fourier Inversion Evaluation for the Tweedie Probability...

In tweedie: Evaluation of Tweedie Exponential Family Models

Fourier Inversion Evaluation for the Tweedie Probability Function

Description

Evaluates the probability density function (pdf) for Tweedie distributions using Fourier inversion, for given values of the dependent variable y, the mean mu, dispersion phi, and power parameter power. Not usually called by general users, but can be used in the case of evaluation problems.

Usage

dtweedie_inversion(y, mu, phi, power, method = 3, verbose = FALSE, 
                          details = FALSE, IGexact = TRUE)

dtweedie.inversion(y, power, mu, phi, method = 3, verbose, details)

Arguments

y	vector of quantiles.
mu	the mean parameter \mu.
phi	the dispersion parameter \phi.
power	scalar; the power parameter p.
method	the method to use; one of 1, 2, or 3 (the default).
verbose	logical; if TRUE, display some internal computation details. The default is FALSE.
details	logical; if TRUE, return a list with basic details of the integration. The default is FALSE.
IGexact	logical; if TRUE (the default), evaluate the inverse Gaussian distribution using the 'exact' values, otherwise uses inversion.

Value

A numeric vector of densities if details=FALSE; if details = TRUE, a list containing denisty (a vector of the values of the density), regions (a vector of the number of integration regions used),method (a vector giving the evaluation method used; see the Note below on the three methods), and exitstatus (a vector, where a 1 for any value means a computational problem or target relative accuracy not reached, for the corresponding observation).

Note

The 'exact' values for the inverse Gaussian distribution are not really exact, but evaluated using inverse normal distributions, for which very good numerical approximation are available in R. For special cases of p (i.e., p = 0, 1, 2, 3), where no inversion is needed, regions and method are set to NA for all values of y. For special cases of y for other values of p (i.e., P(Y = 0)), regions and method are set to NA.

The three methods are described in Dunn & Smyth (2008).

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, 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")}

Examples

# Plot a Tweedie density
y <- seq(0.02, 4, length = 50)
fy <- dtweedie_inversion(y, mu = 1, phi = 1, power = 1.1)
plot(y, fy, type = "l", lwd = 2, ylab = "Density")

tweedie documentation built on Feb. 27, 2026, 9:06 a.m.