Discrete Quantile Estimation

Abstract

We consider estimation of a quantile from a discrete distribution. This gives rise tothree new ideas, the confidence set for such a quantile, the notion that the associatedconfidence level can be increased after the data are collected, and that it is legitimateto strive to obtain a singleton confidence set. We develop properties of the samplequantile noting that the behavior for discrete populations is very different from the behavior for continuous populations. We illustrate the results with simulations andexamples.

Keywords: Quantile estimation, Discrete parameter, Discrete population, Expost confidence, Singleton confidence set