# Uniform Distribution

(redirected from Uniformly distributed)

## uniform distribution

[′yü·nə‚fȯrm ‚di·strə′byü·shən]
(statistics)
The distribution of a random variable in which each value has the same probability of occurrence. Also known as rectangular distribution.
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 It might be outdated or ideologically biased.

## Uniform Distribution

a special type of probability distribution of a random variable X that takes on values in the interval (a - h, a + h). A uniform distribution is characterized by the probability density function

The mathematical expectation is EX = a, the variance is D X= h2/3, and the characteristic function is

By means of a linear transformation the interval (a - h, a + h) can be made to correspond to any given interval. Thus, the variable Y = (X - a + h)/2h is uniformly distributed over the interval (0, 1). Suppose the variables Y1, Y2,.…, Yn are uniformly distributed over the interval (0, 1). When their sum is normalized by the mathematical expectation n/2 and the variance n/12, the distribution law of the normalized sum rapidly approaches a normal distribution as n increases. In fact, the approximation is often sufficient for practical applications even when n = 3.

References in periodicals archive ?
The quartz wackstone and dolomite facies of the ovlerying Wargal Formation indicated good porosity value, however the distribution of quartz wackstone is restricted to western corner of Upper Indus basin, while dolomite facies is uniformly distributed within it.
Perhaps more importantly, the benefits of economic growth are not uniformly distributed over the population.
Development funds should be uniformly distributed to avoid influx of rural population into urban centres like Lahore and Karachi that have grown into unmanageable metropolis.
However, the cash impacts of tax reform will not be uniformly distributed. U.S.
"We feel this will be particularly important in the analysis of rare variants as these are expected to be less uniformly distributed throughout a country.
It can be imagined that the Voronoi cells and the edges of the Delaunay triangles tend to be similar if the particles are uniformly distributed.
This idea is explored in the following three subsections for one-dimensional cases with successively increased complexity and generality: from uniformly distributed coarse-resolution observations with periodic extension to nonuniformly distributed coarse-resolution observations without periodic extension.
La is uniformly distributed in the cathode, and the sharp line near the SDC layer would indicate negligible diffusion into the barrier layer.
As seen in Scheme-1, PAMAM was uniformly distributed on the surface of the Au electrode.
In their scheme, very weak noises uniformly distributed on [-[[delta].sub.1], [[delta].sub.2]] (0 < [[delta].sub.1] [less than or equal to] [[delta].sub.2]) were persistently introduced to only one agent in a divisive group described by HK dynamics, and it was strictly proved that the disagreement in the group was eliminated in finite time.
In the regular microstructure, the network units are uniformly distributed and they have similar sizes, as shown in Figure 1(a): each unit is nearly round and the diameter of the units is 1 [micro]m on average.

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