Convergence in Distribution

  • Sidney I. Resnick
Part of the Modern Birkhäuser Classics book series (MBC)


This chapter discusses the basic notions of convergence in distribution. Given a sequence of random variables, when do their distributions converge in a useful way to a limit? In statisticians’ language, given a random sample \(X_1, \ldots, X_n,\) the sample mean \(\bar{X}_n\) is CAN; that is, consistent and asymptotically normal. This means that \(\bar{X}\) has an approximately normal distribution as the sample size grows. What exactly does this mean?


Central Limit Theorem Weak Convergence Limit Distribution Type Theorem Delta Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Sidney I. Resnick
    • 1
  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

Personalised recommendations