# 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 ?
In this article, the authors considered the problem of deriving the distribution function of the present value of a sequence of cash flows that are discounted using a given stochastic return process.
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The cumulative distribution function of X is F(x) = Pr{X [less than or equal to] x}.
f]([gamma]b) From experimental data it is therefore possible to evaluate that distribution function.
We prove that, for DARA utility functions, Y is riskier than X if and only if G, the cumulative distribution function of Y, can be formed from F, the cumulative distribution function of X by adding a series of MPSA steps to F, under the restrictions stated in the paper.
Lynn Finkel, Managing Director, has assumed responsibility for running the CDO Group, in addition to heading up the Risk Distribution function.
Previous to working at RTM, a multi-unit Arby's franchisee, Odachowski served as Director of International Purchasing and Distribution for Wendy's International, where he provided leadership to the international purchasing and distribution function for 300 restaurants in 32 countries.
A cumulative distribution function F(t) can be used to describe the probability of observing time T less than or equal to a time t.
The estimation of unknown particle shape distribution function Fs based on the estimator of Ft is an ill-posed problem.

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