Mixed-type distribution plots

摘要

Plotting is among the most effective ways to quickly and accurately describe a probability distribution. It makes often complex information accessible, enabling intuition for respective outcomes at a glance. Matters complicate, however, for mixed-type distributions. Mixed-type distributions contain both continuous and discrete components, and accurately portraying those on a single axis can prove difficult-misleading intuition as a consequence of pulling two otherwise disjoint components into focus together. This article examines the challenges of maintaining the simple, concise, and accurate format of traditional probability distribution plots for mixed-type distributions. We illustrate issues arising within this plot classification paradigm, and why a secondary axis is uniquely suited to improve its communication. An algorithm is devised to consistently scale such plots so that they better coincide with intuition. National Football League football starting field position, meteorological data, and financial instruments provide examples demonstrating effectiveness of this plot technique.