{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T03:16:42Z","timestamp":1777778202739,"version":"3.51.4"},"reference-count":16,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T00:00:00Z","timestamp":1519344000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Information Visualization"],"published-print":{"date-parts":[[2019,7]]},"abstract":"<jats:p>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\u2014misleading 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.<\/jats:p>","DOI":"10.1177\/1473871618756584","type":"journal-article","created":{"date-parts":[[2018,2,23]],"date-time":"2018-02-23T07:29:16Z","timestamp":1519370956000},"page":"311-317","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Mixed-type distribution plots"],"prefix":"10.1177","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5902-9738","authenticated-orcid":false,"given":"Christopher","family":"Weld","sequence":"first","affiliation":[{"name":"Department of Applied Science, College of William and Mary, Williamsburg, VA, USA"}]},{"given":"Lawrence","family":"Leemis","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of William and Mary, Williamsburg, VA, USA"}]}],"member":"179","published-online":{"date-parts":[[2018,2,23]]},"reference":[{"key":"bibr1-1473871618756584","volume-title":"The visual display of quantitative information","author":"Tufte ER.","year":"1983"},{"key":"bibr2-1473871618756584","volume-title":"Exploratory data analysis","author":"Tukey JW.","year":"1977"},{"key":"bibr3-1473871618756584","volume-title":"The elements of graphing data","author":"Cleveland WS.","year":"1985"},{"key":"bibr4-1473871618756584","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.01.015"},{"key":"bibr5-1473871618756584","first-page":"1595","volume-title":"Proceedings of the 2017 winter simulation conference","author":"Weld C"},{"issue":"271","key":"bibr6-1473871618756584","first-page":"901","volume":"50","author":"Aitchison J.","year":"1955","journal-title":"J Am Stat Assoc"},{"key":"bibr7-1473871618756584","first-page":"579","volume-title":"Proceedings of the Indian statistical institute golden jubilee international conference","author":"Tweedie M.","year":"1984"},{"key":"bibr8-1473871618756584","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4076(86)90002-3"},{"key":"bibr9-1473871618756584","doi-asserted-by":"publisher","DOI":"10.2307\/1269547"},{"key":"bibr10-1473871618756584","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/66.3.655"},{"key":"bibr11-1473871618756584","doi-asserted-by":"publisher","DOI":"10.2307\/2556125"},{"key":"bibr12-1473871618756584","first-page":"1","volume":"1","author":"Goodell R.","year":"2016","journal-title":"Natl Footb Leag"},{"key":"bibr13-1473871618756584","unstructured":"Horowitz M. nflscrapR: R package for scraping NFL data off their JSON API, https:\/\/github.com\/maksimhorowitz\/nflscrapR (accessed January 2018)."},{"key":"bibr14-1473871618756584","unstructured":"Freepik. American football player silhouettes collection, www.freepik.com\/free-vector\/american-football-player-silhouettes-collection_722363.htm (accessed January 2018)."},{"key":"bibr15-1473871618756584","unstructured":"National Oceanic and Atmospheric Administration. National centers for environmental information, https:\/\/www.ncdc.noaa.gov\/cdo-web\/datasets#GHCND (accessed January 2018)."},{"key":"bibr16-1473871618756584","unstructured":"Damodaran A. Annual returns on Stock, T.bonds and T.bills: 1928\u2013current, http:\/\/pages.stern.nyu.edu\/~adamodar\/New_Home_Page\/datafile\/histretSP.html (accessed January 2018)."}],"container-title":["Information Visualization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1473871618756584","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1473871618756584","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1473871618756584","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:18:56Z","timestamp":1777490336000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1473871618756584"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2,23]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["10.1177\/1473871618756584"],"URL":"https:\/\/doi.org\/10.1177\/1473871618756584","relation":{},"ISSN":["1473-8716","1473-8724"],"issn-type":[{"value":"1473-8716","type":"print"},{"value":"1473-8724","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,2,23]]}}}