Entropía diferencial

Introducción

Def. Variable Aleatoria:

Let X be a random variable with cumulative distribution function . If is continuous, the random variable is said to be continuous.

Let when the derivative is defined. If , is called the probability density function for X.

The set where is called the support set of X.

Definición

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Ejemplos

Distribución uniforme

Nota

The probability density function of the continuous uniform distribution is:

So, if , f(x) = 1/a from 0 to a and 0 elsewhere.

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Distribución normal

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AEP

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Donde

Nota

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Algunas observaciones

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Entropía diferencial y discreta

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Teorema ( vs )

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Ejemplo

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Otro ejemplo

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Entropía diferencial conjunta y condicional

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(soporte conjunto, de x e y)

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Entropía dif. relativa e Información mutua

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Definición general de información mutua

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Refinando P y Q se consigue una sequencia monótonamente creciente
que tiende a .

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Propiedades

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La distribución normal maximiza h para varianza dada

Entropía de una distribución normal multivariada

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Teorema

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