Kaplan-Meier product-limit survival: kmFailure_zero
ProvedActuarialValuation.kmFailure_zeroactuarial-scienceformal-verificationsurvival-product-limit
The estimated failure probability before the first observed event is zero. The full Lean declaration specifies the finite boundaries, exact units and any positivity, independence or regularity assumptions. This is an original derived Actuarial mathematical statement, not a claim of a numbered previously published theorem.
Mathematical relation:
Preamble
import Mathlib.Data.Real.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Definitions.Def_actuarial_kmFailure
Formal statement
namespace ActuarialValuation theorem kmFailure_zero (r d : ℕ → ℝ) : kmFailure r d 0 = 0 := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 267. Society of Actuaries, Mortality Differences by Handedness, Transactions of the Society of Actuaries 45 (1993), p. 267, https://www.soa.org/globalassets/assets/library/research/transactions-of-society-of-actuaries/1990-95/1993/january/tsa93v459.pdf; Kaplan and Meier, Nonparametric Estimation from Incomplete Observations (1958), Journal of the American Statistical Association 53, pp. 457-481. Parent topic: At-risk exposure and deaths with administrative censoring, product-limit survival estimator and Greenwood variance correction. The particular Lean formula is a new finite/real-algebraic formalisation and remains an unproved theorem target if labelled theorem. Relevant published actuarial derivation: https://www.soa.org/globalassets/assets/library/research/transactions-of-society-of-actuaries/1990-95/1993/january/tsa93v459.pdf
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.