Distribution Function

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distribution function

[‚dis·trə′byü·shən ‚fəŋk·shən]
(industrial engineering)

Distribution Function

 

a fundamental concept of statistical mechanics. In classical statistical mechanics the distribution function characterizes the probability density of the distribution of the particles of a statistical system in phase space—that is, with respect to the coordinates qi and momenta pi. In quantum statistical mechanics the distribution function characterizes the probability of a distribution over quantum-mechanical states.

In classical statistical mechanics the distribution function f(p, q, t) defines the probability dw = f(p, q, t) dpdq of finding a system of N particles at a time t in the volume element of phase space dpdq = dp1dq1 . . . dpNdqN around the point p1, q1, . . ., pN, qN. Since the transposition of identical particles does not change the state, the phase volume should be reduced by a factor of N!. Furthermore, it is convenient to convert to a dimensionless volume element of phase space by replacing dpdq with dpdq/N!h3N, where Planck’s constant h determines the minimum cell size in phase space. (See alsoGIBBS DISTRIBUTION.)

References in periodicals archive ?
These probabilities were arranged in order of increasing magnitude and plotted as cumulative distribution functions as shown in Figures 4 and 6.
In order to test if the Pareto power law distribution fits the data well, the complementary cumulative distribution functions (C-CDF) as a function of earthquake magnitude are shown in Fig.
L-1]) by using the cumulative distribution function as a transform function.
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while player b's equilibrium bid is distributed according to the cumulative distribution function
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In this paper we consider a solution to this problem provided that the cumulative distribution function (cdf) of time to failure is known.
Figure 3 presents the first zone (up to 9 m) Cumulative Distribution Function (CDF) of the measurements deviation from the mean value given as the sum of two Normal (Gaussian) functions.

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