# 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 ?
Several properties of the new suggested distribution were derived by using different functions; one of the important functions is distribution function used to check the behavior of the distribution, which is as under.
Commonly the Weibull distribution function is employed for fitting the wind speed distribution.
Figure 1 Distribution Function f(t) = dF(t)/dt Survival Function S(t) = 1 - F(t) Hazard Function h(t) = f(t)/S(t) Relationships S(t) = exp (-H(t)) F(t) = 1 - exp (-H(t)) f(t) = h(t)exp (-H(t))
n] be independent identically distributed random variables with common distribution function F.
A formulation based on an orientation distribution function and its alignment tensors would be more elegant.
In several financial-actuarial problems, one is faced with the determination of the distribution function of random variables of the form
The other strategy, by contrast, seeks to maintain wholesaler formula overrides, with less emphasis on significantly reducing the cost of the wholesale distribution function.
In assessing the reliability of composite structures, the Weibull distribution function has proved to be a useful and versatile means of describing composite material properties data.
For the Cramer-von Mises test, individuals are sampled at random from a population, the value of a random variable is determined for each individual sampled, and an empirical cumulative distribution function is constructed across the range of that variable.
As the physical distribution function received increased attention by top management there will undoubtedly occur a corresponding increase in the more strategic application of the computer to solving creatively transport and distribution problems.
In section IV we present the main results regarding the effect on saving of an increase in risk characterized by a First Degree Stochastic Dominance (FSD) and a Second Degree Stochastic Dominance (SSD) shift of the distribution function of the rate of return.

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