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tweedieDistr provides density, distribution function,
quantile function, and random generation for the Tweedie
distribution under the compound Poisson-Gamma parameterisation
with power parameter \(p \in (1, 2)\).
A distributional-compatible
constructor is also provided for use in tidy modelling workflows. The
Tweedie family naturally combines a point mass at zero with a continuous
positive component, making it well suited to intermittent demand data
and any setting where exact zeros occur alongside strictly positive
observations.
We provide four stats-like functions:
dtweedie(): probability density function via the series
expansion of Dunn & Smyth (2005).ptweedie(): cumulative distribution function using a
truncated compound Poisson-Gamma summation.qtweedie(): quantile function via Newton-Raphson
algorithm, with a fallback to bisection.rtweedie(): random generation via the exact compound
Poisson–Gamma representation.We also provide a single constructor for a distributional
object:
dist_tweedie(): create the vectorised object for the
Tweedie distribution. It supports the standard
distributional interface: density(),
CDF(), quantile(), generate(),
mean(), variance(),
distributional::skewness(),
distributional::kurtosis(), and
distributional::support().You can install the stable version from CRAN:
install.packages("tweedieDistr")You can install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("StefanoDamato/tweedieDistr")stats-style interfaceThe four dtweedie / ptweedie /
qtweedie / rtweedie functions mirror the
conventions of base R distribution functions and support vectorised
arguments.
library(tweedieDistr)
# density at a few points
dtweedie(c(0, 1, 2, 3), mean = 1, dispersion = 2, power = 1.2)
#> [1] 0.53526143 0.18138057 0.14514878 0.07404391
# cumulative probabilities
ptweedie(c(0, 1, 2, 3), mean = 1, dispersion = 2, power = 1.2)
#> [1] 0.5352614 0.6168058 0.7952006 0.9014508
# quantiles
qtweedie(c(0.25, 0.5, 0.75, 0.9), mean = 1, dispersion = 2, power = 1.2)
#> [1] 0.000000 0.000000 1.713588 2.980538
# random samples
rtweedie(4, mean = 1, dispersion = 2, power = 1.2)
#> [1] 0.000000 1.775823 0.000000 2.885415distributional
interfacedist_tweedie() creates a fully-featured
distributional object, compatible with tidy modelling
frameworks such as fable.
library(tweedieDistr)
d <- dist_tweedie(mean = 1, dispersion = 2, power = 1.2)
d
#> <distribution[1]>
#> [1] Tweedie(1, 2, 1.2)
# moments
mean(d)
#> [1] 1
distributional::variance(d)
#> [1] 2
distributional::skewness(d)
#> [1] 1.697056
distributional::kurtosis(d)
#> [1] 3.36
# support
distributional::support(d)
#> <support_region[1]>
#> [1] [0,Inf)
# density and CDF
density(d, at = c(0, 1, 2, 3))
#> [[1]]
#> [1] 0.53526143 0.18138057 0.14514878 0.07404391
distributional::cdf(d, q = c(0, 1, 2, 3))
#> [[1]]
#> [1] 0.5352614 0.6168058 0.7952006 0.9014508
# quantiles
quantile(d, p = c(0.25, 0.5, 0.75, 0.9))
#> [[1]]
#> [1] 0.000000 0.000000 1.713588 2.980538
# random generation
distributional::generate(d, times = 4)
#> [[1]]
#> [1] 1.274467 0.000000 0.000000 0.000000dist_tweedie() supports vectorised arguments, so a whole
column of distribution objects can be constructed at once; this is
crucial as it allows to use the distribution in the tidyverts forecasting pipelines, for
instance.
library(tweedieDistr)
dist_tweedie(
mean = c(1, 2, 0.5),
dispersion = c(2., 0.5, 1),
power = c(1.2, 1.8, 1.5)
)
#> <distribution[3]>
#> [1] Tweedie(1, 2, 1.2) Tweedie(2, 0.5, 1.8) Tweedie(0.5, 1, 1.5)The Tweedie distribution \[Y \sim \mathrm{Tw}(\mu, \phi, \rho)\] with power \(p \in (1, 2)\) is a compound Poisson-Gamma variable: \(Y = \sum_{i=1}^{N} G_i\), where
\[N \sim \mathrm{Poisson}(\lambda), \qquad G_i \sim \mathrm{Gamma}(\alpha, \beta),\]
with
\[\lambda = \frac{\mu^{2-p}}{\phi(2-p)}, \quad \alpha = \frac{2-p}{p-1}, \quad \beta = \frac{1}{\phi(p-1)\mu^{p-1}}.\]
The distribution has mean \(\mu\) and variance \(\phi\mu^p\). When \(N = 0\) the sum is conventionally defined as zero, giving a point mass \(P(X = 0) = e^{-\lambda}\). The density for \(x > 0\) is evaluated via the series expansion of Dunn & Smyth (2005), implemented in C++ through Rcpp and RcppArmadillo.
 Stefano Damato (Maintainer) |
If you encounter a bug, please file a minimal reproducible example on GitHub.
Dunn, P. K., & Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities. Statistics and Computing, 15(4), 267–280. https://doi.org/10.1007/s11222-005-4070-y.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.