Uniform Distribution

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uniform distribution

[′yü·nə‚fȯrm ‚di·strə′byü·shən]
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 It might be outdated or ideologically biased.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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Let U [member of] U(0,1) be a Standard Uniform random variable.
Equal distribution function of the uniform random variable U:
To this end, suppose that [D.sub.m] is a discrete uniform random variable on the first m positive integers, so that its mass function is given by P([D.sub.m] = d) = 1/m for d = 1,2, ..., m, and P([D.sub.m] = d) = 0 otherwise.
Use can then be made of the continuous uniform random variable V with probability density function given by
* Let [mu] be a distribution on R with cumulative distribution function F .If U is uniform on [0,1] then the law of [F.sup.-1](U) is where [F.sup.-1](u) = inf {x | F(x) [greater than or equal to] u} is the right continuous inverse of F; hence to simulate any distribution a uniform random variable on [0,1] is sufficient.
Let U [epsilon] U(0,1) be a Standard Uniform random variable.
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The distribution of the sum of uniform random variables that may have differing domains is found in [18-21].
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In order to establish an approach for evaluating the system reliability of such systems, we assume the loss factors are continuous uniform random variables and generate N uniformly distributed pseudo-random numbers in the interval [0, 1].
Hence N = (1.039921 + 1.006469)/2 = 1.023195 is the average consumption of uniform random variables in Algorithm NA.
The size of an object is therefore a product of independent uniform random variables times X.

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