Theorems · Theorem · probability
ProbabilityTheory.lintegral_gammaPDF_eq_one
∀ {a r : ℝ}, 0 < a → 0 < r → ∫⁻ (x : ℝ), ProbabilityTheory.gammaPDF a r x = 1The pdf of the gamma distribution integrates to 1
- Defined in
- Mathlib.Probability.Distributions.Gamma
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 283 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- MeasureTheory.aeproof · cited by 2,352
- LT.lt.leproof · cited by 2,189
- MeasureTheory.integralproof · cited by 1,779
- mul_assocproof · cited by 1,667
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Set.Ioiproof · cited by 1,463
- LT.lt.ne'proof · cited by 1,417
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isProbabilityMeasure_gammaMeasureproof · cited by 3
- ProbabilityTheory.lintegral_exponentialPDF_eq_oneproof · cited by 0