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.

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 ?
To assess the results, we use a uniform distribution model and repeat the same process to get its D2D average throughput.
where [[xi].sub.1], [[xi].sub.2], ..., [[xi].sub.n] are the random variables satisfying a uniform distribution and [[sigma].sub.1], [[sigma].sub.2], ..., [[sigma].sub.n] are their corresponding uncertainty bounds, respectively.
Let [X.sub.i] for i = 1, 2, ..., n be independent random variables, each having the continuous uniform distribution on the unit interval, and let T = [[summation].sup.n.sub.i=1] [X.sub.i].
(i) First, it is well known that, on a finite measure space, the uniform distribution maximizes entropy: that is, the uniform distribution has the maximal entropy among all probability distributions on a set of finite Lebesgue measures [8].
We expected that these larger Pt-hydroxide clusters would be efficient to improve the durability because the larger cluster size (3-6 nm) in the solution would require a greater distance between each Pt particle or a uniform distribution of the Pt particles on the support material.
Moreover, the dot-chart shows short tail and equally distributed data-concentration for the uniform distribution, medium tails with more data-concentration near the mean than uniform for the normal distribution, long tails with more data-concentration near the mean than normal for the logistic and Laplace distributions.
In this paper, two topics related to the Riemann zeta function will be discussed: uniform distribution on the derivatives of the Riemann zeta function and an application of Birkhoff's ergodic theorem to the Riemann zeta function and its derivatives in connection with affine Boolean transformations.
The five-star Burj Al Arab property in Dubai has launched a new laundry system from Hiemac that has improved the uniform distribution process, making itsmoother, more efficient and easier to manage.
1 (d), although the histogram retains the shapes of the highest peaks, an approximately uniform distribution histogram emerges.
The ministry commended student volunteers who stepped up to help parents in the uniform distribution process.
The water vapor is vented during extrusion, resulting in a uniform distribution of very small additive particles.
This keeps the pellets in constant motion, generates a uniform distribution of thermal energy, and prevents pellets from sticking.

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