Distribution Function

(redirected from Cumulative distribution function)
Also found in: Dictionary, Acronyms, Wikipedia.

distribution function

[‚dis·trə′byü·shən ‚fəŋk·shən]
(industrial engineering)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.)

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
To convert the resulting integral into something that looks like a cumulative distribution function (CDF), it must be expressed in terms of integrals that have lower limits of -[infinity]; thus
Caption: Figure 3: Complementary cumulative distribution functions of the loan scale.
These probabilities were arranged in order of increasing magnitude and plotted as cumulative distribution functions as shown in Figures 4 and 6.
L-1]) by using the cumulative distribution function as a transform function.
Caption: Figure 9: Uncertainty instability failure criterion cumulative distribution functions.
The complementary cumulative distribution function (CCDF) is one of the most frequently used parameters for analyzing PAPR reduction by measuring its distribution.
It was pointed out that any N-dimensional joint cumulative distribution function might be decomposed to N marginal cumulative distributions and one Copula function.
In this paper the unity of cumulative distribution function is divided to two parts using cumulative distribution function under and above the mean to obtain a measure of skewness that is zero for symmetric distributions and to three parts in terms of 50% confidence interval of normal random variable to obtain a measure of data-concentration that is zero for normal distribution.
An agent has outside option r + F, where F is a strictly increasing cumulative distribution function (CDF) with probability density function f The agent faces a decision about whether to steal a good of price p or get the outside option r.
The cumulative distribution function F(x) is shown in Figure 7 (b) and it is the integral of the probability density function f(t) as given in Equation 9.
The cumulative distribution function should be calculated.

Full browser ?