The Logistic Curve and the Logistic Probability Distribution

Pierre François Verhulst (1804-49) developed and named the logistic curve in 1845. Siméon Denis Poisson (1781-1840) created, but did not name, the logistic probability distribution in 1824. Their work had some similarities in form but captured different ideas. Verhulst wrote about population growth, but Poisson contributed to mathematical statistics. The first appearances of the logistic curve and the logistic probability distribution are the subjects of this historical note. Section II contains Verhulst’s theory of population growth after summarizing Thomas Malthus’ (1766-1834) views on population, which provide the environment within which Verhulst lived and worked. Section III summarizes Poisson’s derivation of the logistic probability distribution. The note ends with a conclusion in Section IV.