Other parameters present in the distribution that are not of any interest, or that are already calculated in advance, are called nuisance parameters.
Exponential families have a large number of properties that make them extremely useful for statistical analysis. In the special case that η(θ)=θ and T(x)=x then the family is called a natural exponential family. Further, the Bregman divergence in terms of the natural parameters and the log-normalizer equals the Bregman divergence of the dual parameters (expectation parameters), in the opposite order, for the convex conjugate function. Thenas expected.
5 That Are Proven To Test Functions
(This does emerge correctly when using the form of
A
(
x
)
{\displaystyle A(x)\ }
shown in variant 3. Examples:
Given an exponential family defined by
f
X
(
x
)
=
h
(
x
)
exp
[
T
click for more info (
x
)
A
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)
]
{\displaystyle f_{X}(x\mid \theta )=h(x)\,\exp \!{\bigl [}\,\theta \cdot T(x)-A(\theta )\,{\bigr ]}}
, where
{\displaystyle \Theta }
is the parameter space, such that
R
k
{\displaystyle \theta \in \Theta \subset \mathbb {R} ^{k}}
. .