Codage arithmétique pour la description d'une distribution

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HAL Id: hal-00367577

https://hal.archives-ouvertes.fr/hal-00367577

Submitted on 11 Mar 2009

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Codage arithmétique pour la description d’une distribution

Guilhem Coq, Olivier Alata, Christian Olivier, Marc Arnaudon

To cite this version:

Guilhem Coq, Olivier Alata, Christian Olivier, Marc Arnaudon. Codage arithmétique pour la descrip-

tion d’une distribution. TAIMA, May 2007, Hammamet, Tunisie. pp.65-71. �hal-00367577�

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Codage arithmétique pour la description d'une distribution

HAL Id: hal-00367577

https://hal.archives-ouvertes.fr/hal-00367577

Submitted on 11 Mar 2009

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Codage arithmétique pour la description d’une distribution

Guilhem Coq, Olivier Alata, Christian Olivier, Marc Arnaudon

To cite this version:

Guilhem Coq, Olivier Alata, Christian Olivier, Marc Arnaudon. Codage arithmétique pour la descrip-

tion d’une distribution. TAIMA, May 2007, Hammamet, Tunisie. pp.65-71. �hal-00367577�

1

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j ∈ E ^k i

x ⁿ = x ₁ , . . . , x n

x ⁿ

P(x ⁿ |θ) = 1 m ^k

j∈E ^k

θ(i|j) ^n(i|j)

x ⁿ

x ⁿ ∈ E ⁿ

x ^t = x ₁ , . . . , x _t

θ ˆ ^(t) (i|j) = n ^(t) (i|j) + 1

n ^(t) (j) + m

j ∈ E ^k

n ^(t) (i|j)

n ^(t) (j)

x ^t

n ^(t) (j)

j = x _t−k+1 , . . . , x _t

I _c

θ ˆ ^(t) (i|j)

x _t+1

x ⁿ

1/4 ≤ 2 ⁻² + 2 ⁻⁵ < 7/24

1/4 ≤ 2 ⁻² < 7/24

k = 1 t x ^t I c θ ˆ ⁽ ^t ⁾ (.|.)

(a|b) = 1/2 [0, ¹ ₂ , 1)

a [0, ¹ ₂ ) (a|a) = 1/2

(a|b) = 1/2 [0, ¹ ₄ , ¹ ₂ )

ab [ ¹ ₄ , ¹ ₂ ) (a|a) = 1/3

(a|b) = 1/2 [ ¹ ₄ , ³ ₈ , ¹ ₂ )

aba [ ¹ ₄ , ³ ₈ ) (a|a) = 1/3

(a|b) = 2/3 [ ¹ ₄ , ₂₄ ⁷ , ³ ₈ )

abaa [ ¹ ₄ , ₂₄ ⁷ ) . . . . . .

x ⁿ

x ⁿ

Θ _k

Θ _k

|Θ k | = (m −1)m ^k

x ⁿ

Θ _k

x ⁿ

C _k (x ⁿ )

x ⁿ

k ^?

k ^?

C k (x ⁿ )

C _k (x ⁿ )

IE [C _k (x ⁿ )]