Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fisher Information With Respect to Cumulants   Fisher information is a measure of the best precision with which a parameter
can be estimated from statistical data. It can also be defined for a continuous
random variable without reference to any parameters, in which case it has a
physically compelling interpretation of representing the highest precision with
which the first cumulant of the random variable, i.e., its mean, can be
estimated from its statistical realizations. We construct a complete hierarchy
of information measures that determine the best precision with which all of the
cumulants of a random variable -- and thus its complete probability
distribution -- can be estimated from its statistical realizations. Several
properties of these information measures and their generating functions are
discussed.

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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio