Tweedie

class superglm.Tweedie(p: float)

Bases: object

Tweedie distribution. V(mu) = mu^p, with p in (1, 2).

Parameters:

pfloat

Power parameter. Must be in (1, 2). p → 1 approaches Poisson, p → 2 approaches Gamma.

variance(

mu: NDArray,

) → NDArray

V(μ) = μᵖ.

variance_derivative(

mu: NDArray,

) → NDArray

V’(μ) = p·μᵖ⁻¹.

variance_second_derivative(

mu: NDArray,

) → NDArray

V’’(μ) = p(p-1)·μᵖ⁻². Wood (2011) Appendix D.

deviance_unit(

y: NDArray,

mu: NDArray,

) → NDArray

Tweedie unit deviance evaluated without close-mean cancellation.

log_likelihood(

y: NDArray,

mu: NDArray,

weights: NDArray,

phi: float = 1.0,

) → float

Tweedie log-likelihood via the Dunn–Smyth series.