Differential Entropy
المؤلف:
Cover, T. M. and Thomas, J. A
المصدر:
Elements of Information Theory. New York: Wiley, 1991.
الجزء والصفحة:
...
12-11-2021
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Differential Entropy
Differential entropy differs from normal or absolute entropy in that the random variable need not be discrete. Given a continuous random variable 
with a probability density function 
, the differential entropy 
is defined as
 |
(1)
|
When we have a continuous random vector 
that consists of 
random variables 
, 
, ..., 
, the differential entropy of 
is defined as the 
-fold integral
where 
is the joint probability density function of 
.
Thus, for example, the differential entropy of a multivariate Gaussian random variate 
with covariance matrix 
is
Additional properties of differential entropy include
 |
(6)
|
where 
is a constant and
 |
(7)
|
where 
is a scaling factor and 
is a scalar random variable. The above property can be generalized to the case of a random vector 
premultiplied by a matrix 
,
 |
(8)
|
where 
is the determinant of matrix 
.
REFERENCES:
Cover, T. M. and Thomas, J. A. Elements of Information Theory. New York: Wiley, 1991.
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