Editing Asymptotic analysis (section)

== Asymptotic distribution ==
{{main|Asymptotic distribution}}

In [[mathematical statistics]], an '''[[asymptotic distribution]]''' is a hypothetical distribution that is in a sense the "limiting" distribution of a sequence of distributions. A distribution is an ordered set of random variables {{math|''Z''<sub>''i''</sub>}} for {{math|1=''i'' = 1, …, ''n''}}, for some positive integer {{math|''n''}}. An asymptotic distribution allows {{math|''i''}} to range without bound, that is, {{math|''n''}} is infinite.

A special case of an asymptotic distribution is when the late entries go to zero—that is, the {{math|''Z''<sub>''i''</sub>}} go to 0 as {{math|''i''}} goes to infinity. Some instances of "asymptotic distribution" refer only to this special case.

This is based on the notion of an [[asymptotic]] function which cleanly approaches a constant value (the ''asymptote'') as the independent variable goes to infinity; "clean" in this sense meaning that for any desired closeness epsilon there is some value of the independent variable after which the function never differs from the constant by more than epsilon.

An [[asymptote]] is a straight line that a curve approaches but never meets or crosses. Informally, one may speak of the curve meeting the asymptote "at infinity" although this is not a precise definition. In the equation <math>y = \frac{1}{x},</math> ''y'' becomes arbitrarily small in magnitude as ''x'' increases.