Convergence in distribution
From Encyclopedia of Mathematics
Convergence of a sequence of random variables defined on a certain probability space
, to a random variable
, defined in the following way:
if
![]() | (*) |
for any bounded continuous function . This form of convergence is so called because condition (*) is equivalent to the convergence of the distribution functions
to the distribution function
at every point
at which
is continuous.
Comments
See also Convergence, types of; Distributions, convergence of.
This is special terminology for real-valued random variables for what is generally known as weak convergence of probability measures (same definition as in (*), but with ,
taking values in possibly more general spaces).
How to Cite This Entry:
Convergence in distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_distribution&oldid=19094
Convergence in distribution. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Convergence_in_distribution&oldid=19094
This article was adapted from an original article by V.I. Bityutskov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article