Package 'tweedieDistr'

Tweedie Distribution

Description

Construct a Tweedie distribution object using the compound Poisson–Gamma parameterisation with power parameter in $(1, 2)$. The Tweedie family is a subclass of exponential dispersion models that naturally produces exact zeros (via the Poisson count component) mixed with continuous positive values (via the Gamma severity component), making it well suited to intermittent demand data.

Usage

dist_tweedie(mean = 1, dispersion = 1, power = 1.5)

Arguments

mean	Mean parameter $\mu > 0$.
dispersion	Dispersion parameter $\phi > 0$.
power	Power parameter $p \in (1, 2)$.

Details

The density is evaluated using the series expansion of Dunn & Smyth (2005), implemented in C++ for performance.

Value

A distributional distribution object of class dist_tweedie.

References

Dunn, P. K., & Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities. Statistics and Computing, 15(4), 267–280. doi:10.1007/s11222-005-4070-y.

Examples

d <- dist_tweedie(mean = 2, dispersion = 0.8, power = 1.5)
d |> mean()
d |> quantile(c(0.5, 0.9))
d |> density(c(0, 1.5, 3))
d |> distributional::variance()
d |> distributional::generate(10)

---

Tweedie Distribution Functions

Description

Density, distribution function, quantile function and random generation for the Tweedie distribution with mean equal to mean, dispersion equal to dispersion, and power equal to power.

Usage

rtweedie(n, mean = 1, dispersion = 1, power = 1.5)

dtweedie(x, mean = 1, dispersion = 1, power = 1.5, log = FALSE)

ptweedie(
  q,
  mean = 1,
  dispersion = 1,
  power = 1.5,
  lower.tail = TRUE,
  log.p = FALSE
)

qtweedie(
  p,
  mean = 1,
  dispersion = 1,
  power = 1.5,
  lower.tail = TRUE,
  log.p = FALSE
)

Arguments

n	number of observations. If length(n) > 1, the length is taken to be the number required.
mean	vector of means.
dispersion	vector of dispersion parameters.
power	vector of power parameters.
x, q	vector of quantiles.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are $P[X \le x]$; otherwise, $P[X > x]$.
p	vector of probabilities.

Details

If mean, dispersion, or power are not specified they assume the default values of 1, 1, and 1.5, respectively.

The Tweedie distribution used here follows the compound Poisson-Gamma parameterisation with power parameter in $(1, 2)$. It has $\mathbb{E}[X] = \mu$ and $\mathrm{Var}(X) = \phi\mu^p$, where $\mu$ is mean, $\phi$ is dispersion, and $p$ is power.

Value

dtweedie gives the density, ptweedie gives the distribution function, qtweedie gives the quantile function, and rtweedie generates random samples.

The length of the result is determined by n for rtweedie, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

References

Dunn, P. K., & Smyth, G. K. (2005). Series evaluation of Tweedie exponential dispersion model densities. Statistics and Computing, 15(4), 267–280. doi:10.1007/s11222-005-4070-y.

---