Documentation

Lean 4 Proof

theorem escortRawMoment_hasDerivAt [NeZero J]
    (x : Fin J → ℝ) (hx : ∀ j, 0 < x j) (ρ : ℝ) (n : ℕ) :
    HasDerivAt (fun p => escortRawMoment x p n)
      (escortRawMoment x ρ (n + 1) -
       escortRawMoment x ρ n * escortRawMoment x ρ 1) ρ := by
  unfold escortRawMoment
  have hZ := ne_of_gt (escortPartitionZ_pos x hx ρ)
  have hquot := (escortPartitionZn_hasDerivAt x hx ρ n).div
    (escortPartitionZ_hasDerivAt x hx ρ) hZ
  refine hquot.congr_deriv ?_
  rw [← escortPartitionZn_one]
  field_simp

Dependency Graph

Used by

Location

thesis/CESProofs/Foundations/CumulantTower.lean:139

Module Section

The Cumulant Tower: Higher-Order Bridges Between CES and Escort Statistics

In the same file