| Abstract: | A sequence of independent, identically distributed random variables is considered. Given a simple local condition on the distribution of these random variables, we give necessary and sufficient conditions on the tails of the distribution for the moment generating function of a standardized quantile of the first n observations to converge to the moment generating function of an appropriate normal distribution as n →infinity;. This result is actually a special case of a more general result which can also be used to show convergence in distribution and convergence of moments of standardized quantiles. |
