Confidence intervals for discrete distributions based on a single observation

Confidence intervals are developed for the mode of a discrete unimodal distribution in the case where only a single observation is available. These intervals are centered on either the observation, X, or a weighted average of X with a constant, b, chosen by the investigator. Intervals are derived for nonrestricted unimodal distributions, for unimodal distributions with a symmetry property, and for a family of two-sided truncated geometric distributions.