Theorems · Theorem · probability
ProbabilityTheory.gammaPDF_of_nonneg
∀ {a r x : ℝ},
0 ≤ x → ProbabilityTheory.gammaPDF a r x = ENNReal.ofReal (r ^ a / Real.Gamma a * x ^ (a - 1) * Real.exp (-(r * x)))- Defined in
- Mathlib.Probability.Distributions.Gamma
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 257 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Real.expstatement and proof · cited by 871
- ENNReal.ofRealstatement and proof · cited by 863
- Real.Gammastatement and proof · cited by 76
- ProbabilityTheory.gammaPDFstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.lintegral_gammaPDF_eq_oneproof · cited by 2