definition 11.42 Characteristic function

Rests on

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Supports

• depends_on lemma A.197 The transform is differentiable at the origin ¶
• depends_on lemma A.179 Truncation estimate ¶
  • depends_on lemma A.180 Tightness ¶
• depends_on lemma 11.44 Second-order expansion ¶
  • depends_on theorem 11.46 Central limit theorem, Lindeberg–Lévy ¶
    • depends_on phenomenon 115.44 A large-scale dipole above $8\times10^{18}$ electronvolts ¶
    • 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 theorem 11.48 Lindeberg–Feller ¶
• depends_on proposition 11.43 Elementary properties ¶
  • depends_on lemma A.200 Transform estimate ¶
  • depends_on proposition 11.81 Density, mean and variance ¶
    • depends_on corollary 11.84 Residuals about a weighted mean; the Birge ratio ¶
    • depends_on example 33.15 The six values are mutually inconsistent, and by how much ¶
      • depends_on phenomenon 33.16 The least well determined of the constants ¶
  • 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 11.46 Central limit theorem, Lindeberg–Lévy ¶ ↺
• depends_on proposition 11.81 Density, mean and variance ¶ ↺
• depends_on theorem A.192 Berry–Esseen ¶
• depends_on theorem A.168 Lévy's continuity theorem ¶
  • depends_on corollary A.181 The converse ¶
• depends_on theorem A.177 Fourier inversion for a distribution function ¶
  • depends_on corollary A.178 The characteristic function determines the distribution ¶
    • depends_on lemma A.220 At each point, field and derivative are independent Gaussians ¶
  • depends_on lemma A.196 Inversion for a difference ¶
    • depends_on theorem A.198 Esseen's smoothing inequality ¶
• depends_on theorem A.183 Lindeberg–Feller ¶ ↺
• depends_on theorem 11.45 Lévy's continuity theorem ¶
  • depends_on theorem 11.46 Central limit theorem, Lindeberg–Lévy ¶ ↺
  • depends_on theorem 11.48 Lindeberg–Feller ¶ ↺