Editing Logistic distribution (section)

=== Physics ===
The PDF of this distribution has the same functional form as the derivative of the [[Fermi function]]. In the theory of electron properties in semiconductors and metals, this derivative sets the relative weight of the various electron energies in their contributions to electron transport. Those energy levels whose energies are closest to the distribution's "mean" ([[Fermi level]]) dominate processes such as electronic conduction, with some smearing induced by temperature.<ref>{{Cite book | isbn = 9780521484916 | title = The Physics of Low-dimensional Semiconductors: An Introduction | last1 = Davies | first1 = John H. | year = 1998 | publisher = Cambridge University Press  }}</ref>{{rp|34}} However the pertinent ''probability'' distribution in [[Fermi–Dirac statistics]] is actually a simple [[Bernoulli distribution]], with the probability factor given by the Fermi function.

The logistic distribution arises as limit distribution of a finite-velocity damped random motion described by a telegraph process in which the random times between consecutive velocity changes have independent exponential distributions with linearly increasing parameters.<ref>A. Di Crescenzo, B. Martinucci (2010) "A damped telegraph random process with logistic stationary distribution", ''[[Applied Probability Trust|J. Appl. Prob.]]'', vol. 47, pp. 84–96.</ref>