# 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.
The following graphical representations for Probability Density Function, Cumulative Distribution Function, Survival Function, Hazard Rate Function and Reverse Hazard Rate Function of DWD given below, with different shape and scale parameters.
alpha]/2], df) is the Student's t-inverse cumulative distribution function using degrees of freedom for the corresponding confidence.
Note that we will focus our attention on the cumulative distribution function rather than the standard probability distribution function as it exhibits an extra degree of regularity while still containing the same amount of information about the global distribution of the values of a given function.
The results of their study also present the cumulative distribution function versus ESD measured voltages in various intervals.
while player b's equilibrium bid is distributed according to the cumulative distribution function
The Gumbel distribution is thin-tailed for which all moments are finite and whose cumulative distribution function declines exponentially in the tails.
In equation (1) F(y) is the cumulative distribution function of Kappa distribution given we follow the methodology of U-statistic introduced by Hoeffding [9].
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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