Parameter measurability for the Gamma distribution #
Joint measurability in shape and rate lets measurable parameter maps produce measurable measure-valued Gamma families, in particular kernels.
theorem
TauCeti.Probability.measurable_uncurry_gammaPDF :
Measurable fun (q : (ℝ × ℝ) × ℝ) => ProbabilityTheory.gammaPDF q.1.1 q.1.2 q.2
The Gamma density is measurable jointly in its shape, its rate and the point.
theorem
TauCeti.Probability.measurable_gammaMeasure :
Measurable fun (p : ℝ × ℝ) => ProbabilityTheory.gammaMeasure p.1 p.2
The Gamma family is measurable in its parameters.