The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Central Limit Theorems

  • Werner Ploberger
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2628

Abstract

Central limit theorems describe the behaviour of distributions of sums of random variables. We start with the classical result of distributions of sums of independent random variables converging to the Gaussian (bell-curve) distribution. We describe the most important cases of convergence to Gaussian distributions (sums of martingale differences) as well as convergence to other distributions.

Keywords

Central limit theorems Convergence Edgeworth expansions Feller condition Laplace, P. S. Lindeberg condition Long-term variance Lyapunov condition Martingale differences Maximum likelihood Monte Carlo simulation 
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Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Werner Ploberger
    • 1
  1. 1.