Asymptotic theory

Asymptotic theory or large-sample theory is the branch of mathematics which studies asymptotic expansions.

An example of an asymptotic result is the prime number theorem: Let π(x) be the number of prime numbers that are smaller than or equal to x. Then the limit

exists, and it is equal to 1.

Asymptotic theory ("asymptotics") is used in several mathematical sciences. In statistics, asymptotic theory provides limiting approximations of the probability distribution of sample statistics, such as the likelihood ratio statistic and the expected value of the deviance. Asymptotic theory does not provide a method of evaluating the finite-sample distributions of sample statistics, however. Non-asymptotic bounds are provided by methods of approximation theory.

In mathematics and 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

for ${\displaystyle i=1}$ to ${\displaystyle n}$ for some positive integer ${\displaystyle n}$. An asymptotic distribution allows ${\displaystyle i}$ to range without bound, that is, ${\displaystyle n}$ is infinite.

...
Wikipedia