Last Updated：2022/12/22
Sentence
The
‘smoothness’
of
distributions
can
be
understood
in
various
senses,
this
is
why
we
used
quotation
marks
before;
further
we
will
drop
them.
The
smoothness
can
be
understood
as
the
differentiability
of
the
distribution
function,
boundedness
of
some
of
its
derivatives,
the
existence
of
the
absolutely
continuous
component,
the
decrease
of
the
characteristic
function
with
a
certain
rate,
the
validity
of
the
Cramér
condition,
the
condition
𝜎(𝛷)→0
as
n→∞,
etc.
Quizzes for review
The ‘smoothness’ of distributions can be understood in various senses, this is why we used quotation marks before; further we will drop them. The smoothness can be understood as the differentiability of the distribution function, boundedness of some of its derivatives, the existence of the absolutely continuous component, the decrease of the characteristic function with a certain rate, the validity of the Cramér condition, the condition 𝜎(𝛷)→0 as n→∞, etc.
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