- Density, cumulative distribution function and quantiles for the Tweedie distributions.
Includes the normal, Poison, Poison-gamma and inverse-Gaussian distributions as special
- dtweedie(x, mu, phi=1, power=1.5)
ptweedie(q, mu, phi=1, power=1.5)
qtweedie(p, mu, phi=1, power=1.5)
- REQUIRED ARGUMENTS
||vector of deviate values. Missing values (NAs) are allowed.
||vector of probabilities. Missing values (NAs) are allowed.
||vector of quantiles. Missing values (NAs) are allowed.
||vector of (positive) means.
- OPTIONAL ARGUMENTS
||vector of (positive) dispersion parameters.
||power index of variance function. The variance of the distribution is phi*mupower
- Vector of same length as x, p or q giving the density (dpoisgam),
probability (ppoisgam) or quantile (ppoisgam) for the Poisson gamma
distribution with mean mu, dispersion phi and index power.
Elements of x, p or q that are missing will cause the corresponding
elements of the result to be missing.
The variance power p characterizes the distribution of x.
The following are some special cases:
||Compound Poisson, non-negative with mass at zero
||Stable, with support on the positive reals
The name Tweedie has been associated with this family by Jørgensen in
honour of M. C. K. Tweedie.
- Jørgensen, B. (1987). Exponential dispersion models. J. R. Statist. Soc. B, 49,
- Jørgensen, B. (1997). Theory of Dispersion Models, Chapman and Hall, London.
- Smyth, G. K. (1996). Regression modelling of quantity data with exact zeroes. Proceedings
of the Second Australia-Japan Workshop on Stochastic Models in Engineering, Technology and
Management. Technology Management Centre, University of Queensland, 572-580. (Postscript file)
- Tweedie, M. C. K. (1984). An index which distinguishes between some important
exponential families. In 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.
- For some values of index, the results are based on a simple normal approximation which
is very crude. dtweedie and ptweedie
are accurate for p=0,[1,2],3. qtweedie is accurate for
- SEE ALSO
- Tweedie family, Poison-gamma
distribution, inverse-Gaussian distribution
- y <- c(-1,0,4,5,10000)
- d <- dtweedie(y,mu=4,phi=1,power=1.6)
- p <- ptweedie(y,mu=4,phi=1,power=1.6)
Copyright © 1996-2003. Last modified:
24 December 2002