The tail of the cumulative probability distribution of observing a given count in the PSTH becomes a stretched exponential at Hölder exponent

*H* = 0.5. (

*A*) The tails of the cumulative probability distribution, plotted as 1 −

*F*(

*x*) vs.

*x*, for Hölder exponents 0.4, 0.45, 0.5, 0.55, and 0.6 (right to left). The probability distribution is minus the derivative of these curves. Superposed on the data (black) a fit to the last 10

^{5} data points in the cumulative, i.e., the higher 2% percentile (red), in the form

. (

*B–D*) The coefficients

*a*,

*b*, and

*c* for the aforementioned fit, plotted as a function of the Hölder exponent

*H*.

*B* is

*a*, the linear coefficient defining exponential convergence;

*C* is

*b*; and

*D* is

*c*. Notice that the linear component

*a* is (numerically) zero for

*H* < 0.5, exposing the

term as the next higher order. For

*H* > 0.5, the positive linear term guarantees convergence of all moments of the distribution.

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