definition 11.21 Distribution function

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:585 · p. 377

ground object -- no derivation owed

Rests on

depends_on definition 11.20 Density ¶
- depends_on definition 7.39 Darboux sums and the definite integral ¶
  - depends_on axiom 7.1 Completeness of $\R$ ¶

Supports

depends_on definition A.174 Tightness ¶
- depends_on lemma A.175 Tightness makes the Helly limit proper ¶
- depends_on lemma A.180 Tightness ¶
depends_on lemma 11.52 Slutsky ¶
- depends_on theorem A.206 Cramér–Wold, and continuous mapping ¶
  - depends_on lemma A.208 The three averages ¶
    - depends_on corollary A.210 Uniform quadratic approximation on the $n^{-1/2}$ scale ¶
      - depends_on lemma A.213 The three minima ¶
    - depends_on lemma A.211 Root-$n$ localisation ¶
      - depends_on lemma A.213 The three minima ¶ ↺
  - depends_on theorem A.214 Wilks, $k$ parameters and $r$ constraints ¶
- depends_on theorem 11.67 Asymptotics of the MLE ¶
  - depends_on proposition 11.72 Nuisance parameters cost information ¶
  - depends_on theorem 11.88 Wilks ¶
    - depends_on corollary 11.89 Degrees of freedom with nuisance parameters ¶
      - depends_on example 11.107 Degrading a local five sigma ¶
      - depends_on proposition 11.93 $Z=\sqrt{q}$ ¶
      - depends_on remark 11.90 Failure I: a parameter on the boundary ¶
- depends_on theorem 11.88 Wilks ¶ ↺
depends_on proposition 11.22 Properties of the distribution function ¶
- depends_on proposition 11.27 Probability integral transform ¶
depends_on theorem A.168 Lévy's continuity theorem ¶
- depends_on corollary A.181 The converse ¶
depends_on theorem A.173 Helly's selection theorem ¶
- depends_on lemma A.176 Helly–Bray ¶
  - depends_on corollary A.181 The converse ¶ ↺
- depends_on lemma A.175 Tightness makes the Helly limit proper ¶ ↺
depends_on theorem A.206 Cramér–Wold, and continuous mapping ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Density	declared	parts/02-mathematical-methods/09-probability-statistics.tex:592
`depends_on`	←	Tightness	declared	appendices/A-long-proofs.tex:9105
`depends_on`	←	Slutsky	declared	parts/02-mathematical-methods/09-probability-statistics.tex:1443
`depends_on`	←	Properties of the distribution function	declared	parts/02-mathematical-methods/09-probability-statistics.tex:602
`depends_on`	←	Lévy's continuity theorem	declared	appendices/A-long-proofs.tex:8883
`depends_on`	←	Helly's selection theorem	declared	appendices/A-long-proofs.tex:9038
`depends_on`	←	Cramér–Wold, and continuous mapping	declared	appendices/A-long-proofs.tex:10483