Convergence in Distribution
when the distribution functions satisfy at every continuity point of .
Definition 5.6 (Convergence in Distribution)
A sequence of random variables converges to in distribution as and we write
for all where is continuous.
Convergence in probability implies convergence in distribution
Proposition 5.7
If , then .
Related
Stated in
- Definition 5.6 (Convergence in Distribution)§5.2 Central Limit Theorem
- Proposition 5.7§5.2 Central Limit Theorem