theorem 11.103 Level dependence of the mean upcrossing count

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:3176 · p. 408

Rests on

depends_on definition 11.100 Upcrossings ¶
- depends_on definition 11.96 Local, global, trials factor ¶
  - depends_on definition 11.75 $p$-value ¶
    - depends_on definition 11.74 Hypotheses and tests ¶
      - depends_on definition 11.53 Statistical model ¶
  - depends_on equation 11.89 eq:prob-p-one-sided ¶
  - depends_on equation 11.88 eq:prob-q0 ¶
depends_on theorem 11.102 Rice's formula ¶
- depends_on definition 11.28 Gaussian distribution ¶
  - depends_on definition 11.20 Density ¶
    - depends_on definition 7.39 Darboux sums and the definite integral ¶
      - depends_on axiom 7.1 Completeness of $\R$ ¶
- depends_on definition 11.100 Upcrossings ¶ ↺
- proves proof ch:09-probability-statistics@prooflink-5 ¶
proves proof ch:09-probability-statistics@proof-45 ¶

Supports

depends_on corollary 11.105 Trials factor at high significance ¶
depends_on example 11.107 Degrading a local five sigma ¶

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`	→	Upcrossings	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3186
`depends_on`	→	Rice's formula	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3186
`depends_on`	←	Trials factor at high significance	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3236
`depends_on`	←	Degrading a local five sigma	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3350
`proves`	←	ch:09-probability-statistics@proof-45	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3189