# Divergence of sample quantiles - Mathematics > Statistics Theory

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Abstract: We show that the left right sample quantile tends to the left rightdistribution quantile at p in 0,1, if the left and right quantiles areidentical at p. We show that the sample quantiles diverge almost surelyotherwise. The latter can be considered as a generalization of the well-knownresult that the sum of a random sample of a fair coin with 1 denoting heads and-1 denoting tails is 0 infinitely often. In the case that the sample quantilesdo not converge we show that the limsup is the right quantile and the liminf isthe left quantile.

Author: ** Reza Hosseini**

Source: https://arxiv.org/