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In page Logistic distribution:
"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.[1]:34 Note however that the pertinent probability distribution in Fermi–Dirac statistics is actually a simple Bernoulli distribution, with the probability factor given by the Fermi function.
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