What is "logistic" about the logistic distribution, in a common sense way? What is the etymology of and the lexical rationale for the name, not just pure math definition?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The source document for the name "logistic" seems to be this 1844 presentation by P.-F. Verhulst, "Recherches mathématiques sur la loi d'accroissement de la population," in NOUVEAUX MÉMOIRES DE L'ACADÉMIE ROYALE DES SCIENCES ET BELLES-LETTRES DE BRUXELLES, vol. 18, p 1.
He differentiated what we would now call exponential growth of population when resources are essentially unlimited (as seen for example in the growth of the US population in the late 18th and early 19th centuries) from the slower growth when resource limits begin to be reached.
What we call exponential growth, however, he called a "logarithmique" curve (page 6).
He then developed a formula for population growth in the presence of resource limits, and said of the resulting curve:
"Nous donnerons le nom de logistique à la courbe..." which I translate as "We call the curve logistic..." (original emphasis).
That would seem to be intended to distinguish this growth pattern from the "logarithmique" growth in the absence of resource limits, as the figure at the end of the paper illustrates.
The specific form of the equation presented by Verhulst allows for an arbitrary upper asymptote (eq. 5, page 9), while the form we know and love in statistics is the specific case with an asymptote of 1.
The logistic distribution is not a common distribution in analysis, but it ties together the notion of a latent underlying continuous variable which is thresholded in binary outcomes. It turns out that thresholding a logistic RV (to 1 if the RV is greater than some unknown value and 0 otherwise) and calculating a maximum likelihood leads to logistic regression. Contrast this approach with thresholding a normally distributed random variable which leads to probit regression. Applying multiple thresholds leads to cumulative link models.
Now, if your question concerned logistic regression, the term was coined by David Cox in 1958 "The regression analysis of binary sequences (with discussion)" in JRRS. He used the term to the logistic, sigmoidal shape of the modeled mean. For describing the process of a curve which models probabilities that accumulate according to a probabilistically sound way, the term "logistic" is an intuitive choice and the nomenclature stuck.