Lindeberg's condition

In probability theory, Lindeberg's condition is a sufficient condition (and under certain conditions also a necessary condition) for the central limit theorem (CLT) to hold for a sequence of independent random variables.[1][2][3] Unlike the classical CLT, which requires that the random variables in question have finite variance and be both independent and identically distributed, Lindeberg's CLT only requires that they have finite variance, satisfy Lindeberg's condition, and be independent. It is named after the Finnish mathematician Jarl Waldemar Lindeberg.[4]

  1. ^ Billingsley, P. (1986). Probability and Measure (2nd ed.). Wiley. p. 369. ISBN 0-471-80478-9.
  2. ^ Ash, R. B. (2000). Probability and measure theory (2nd ed.). p. 307. ISBN 0-12-065202-1.
  3. ^ Resnick, S. I. (1999). A probability Path. p. 314.
  4. ^ Lindeberg, J. W. (1922). "Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung". Mathematische Zeitschrift. 15 (1): 211–225. doi:10.1007/BF01494395. S2CID 119730242.