Discrete Quantile Estimation

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