Journal of Statistical Theory and Practice

, Volume 7, Issue 2, pp 401–420 | Cite as

Connecting Logistic Probability Models With Basic Dynamic Processes

  • Jeremy A. LauerEmail author
  • Sander Greenland


The logistic distribution is a popular probability model yet it is usually not motivated with reference to the processes under study. While its popularity can be attributed to its simplicity, it can also be derived from basic contextual considerations. Although it has been shown that logistic growth is the limiting form of a class of Markov processes on a lattice, the connections of these microscopic models with statistics are less widely appreciated. We review some history of logistic distributions in classical models of infection, and describe how the apparent density dependence emerges as a consequence of a particular lattice embedding. We then review how logistic growth arises from microscopic random behavior. We also derive a “square-logistic” model from basic considerations. Finally, we describe how the underlying discrete model relates to ordinary logistic regression modeling of time dependence.


Logistic Logit Contact process Percolation Hydrodynamic limit Interacting particle system Lattice Diffusion Hyperbolic differential equation Hyperbolic conservation law Infection Transmission 

AMS 2000 Subject Classifications

Primary 60J70 Secondary 35L40 60K35 62-09 62E10 62J05 62J12 62M05 92D25 92D30 92D40 


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Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.Department of Health Systems FinancingWorld Health OrganizationGeneva 27Switzerland
  2. 2.Department of Epidemiology and Department of StatisticsUniversity of California Los AngelesLos AngelesUSA

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