## Quick Reference

A sequence of random variables *x*_{1},…, *x*_{n},… with corresponding distribution functions *F*_{1}(*x*),…*F*_{n}(*x*),… converges in distribution (or weakly) to the random variable *x* with distribution function *F*(*x*) if the sequence of the corresponding distribution functions converges to *F* at all continuity points of *F*for every ε > 0 starting from some *n*. The distribution given by *F*(*x*) is called the limiting or the asymptotic distribution of *x*_{n}. This concept allows the approximation of the unknown distribution *F*_{n}(*x*) of an estimator or a test statistic with a known asymptotic distribution *F*(*x*). If *x* = *θ* is a constant the limiting distribution is degenerate, i.e. collapses to a single point. In this case (but not in general) convergence in distribution also implies convergence in probability.

*Subjects:*
Economics.