definition 11.28 Gaussian distribution

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:721 · p. 379

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 $\R$ ¶

depends_on definition A.218 The hypotheses ¶
- depends_on lemma A.220 At each point, field and derivative are independent Gaussians ¶
- depends_on theorem A.219 Rice's formula ¶
  - depends_on corollary A.227 The stationary case ¶
depends_on lemma A.226 The level factor ¶
depends_on lemma A.225 The mean positive part ¶
depends_on proposition 11.29 Gaussian moments ¶
depends_on theorem A.192 Berry–Esseen ¶
depends_on theorem A.183 Lindeberg–Feller ¶
- depends_on corollary A.188 Lindeberg–Lévy is the special case ¶
- depends_on corollary A.189 Lyapunov's condition ¶
depends_on theorem 11.102 Rice's formula ¶
- depends_on theorem 11.103 Level dependence of the mean upcrossing count ¶
  - depends_on corollary 11.105 Trials factor at high significance ¶
  - depends_on example 11.107 Degrading a local five sigma ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Density	declared	parts/02-mathematical-methods/09-probability-statistics.tex:732
`depends_on`	←	The hypotheses	declared	appendices/A-long-proofs.tex:11091
`depends_on`	←	The level factor	declared	appendices/A-long-proofs.tex:11382
`depends_on`	←	The mean positive part	declared	appendices/A-long-proofs.tex:11351
`depends_on`	←	Gaussian moments	declared	parts/02-mathematical-methods/09-probability-statistics.tex:740
`depends_on`	←	Berry–Esseen	declared	appendices/A-long-proofs.tex:9845
`depends_on`	←	Lindeberg–Feller	declared	appendices/A-long-proofs.tex:9461
`depends_on`	←	Rice's formula	declared	parts/02-mathematical-methods/09-probability-statistics.tex:3149