Exponential Distribution
Among probability distributions
which are nonzero over a
semi-infinite range of values
and having a finite
mean
, the exponential distribution has maximum entropy.
To the previous case, we add the new constraint
![]() |
(D.39) |
resulting in the objective function

Now the partials with respect to
are

and
is of the form
. The
unit-area and finite-mean constraints result in
and
, yielding
![]() |
(D.40) |
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Gaussian Distribution
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Uniform Distribution