Theorems · Theorem · probability
ProbabilityTheory.gammaPDFReal_nonneg
∀ {a r : ℝ}, 0 < a → 0 < r → ∀ (x : ℝ), 0 ≤ ProbabilityTheory.gammaPDFReal a r xThe gamma pdf is nonnegative
- 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.
Cites10
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
- Nat.cast_zeroproof · cited by 1,870
- le_of_ltproof · cited by 1,175
- mul_nonnegproof · cited by 397
- div_posproof · cited by 337
- Real.exp_posproof · cited by 169
- Real.rpow_pos_of_posproof · cited by 155
- Real.rpow_nonnegproof · cited by 111
- Real.Gamma_pos_of_posproof · cited by 17
- ProbabilityTheory.gammaPDFRealstatement · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cdf_gammaMeasure_eq_integralproof · cited by 1
- ProbabilityTheory.exponentialPDFReal_nonnegproof · cited by 0