Rayleigh distribution

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Rayleigh distribution

[′rā·lē ‚dis·trə‚byü·shən]
A normal distribution of two uncorrelated variates with the same variance.

Rayleigh Distribution


The Rayleigh distribution of the probabilities of the random variable X is characterized by the probability density function

The distribution function is

The mathematical expectation is Rayleigh Distributionand the variance is DX = (4 - π)σ4/2. The maximum value of the density function is equal to Rayleigh Distributionand is reached when x= σ. Curves of the density function for various σ are shown in Figure 1.

Figure 1

The Rayleigh distribution is encountered in applications of probability theory to, for example, radio engineering. The distribution was introduced by Lord Rayleigh in 1880 in connection with the problem of interference of harmonic oscillations with spiral phases.

Rayleigh distribution

A curve that yields a good approximation to the actual labour curves on software projects.

References in periodicals archive ?
It illustrates the Rayleigh distribution which is slightly similar to ZF approach, outperforms the Rician channel model.
To the best of our knowledge, the effects of the no wireless radio fading models other than the Rayleigh distribution have been considered in the performance of the adaptive networks [1]-[4], while it is a very important issue.
Since we model each interfering signal with Rayleigh distribution, with PDF expressed as
[[alpha].sub.n,1] and [[alpha].sub.n,2] are the channel coefficients following Rayleigh distribution, and [[xi].sub.i] is the Gaussian noise, which follows Gaussian distribution with zero mean and variance [N.sub.0]/2.
As a consequence, the norm of [DELTA]C then approximately follows a Rayleigh distribution. Hence, we fitted a Rayleigh distribution to the results, obtaining as output the desired PDF of [DELTA]C.
Rayleigh distribution. We assume that fading coefficients are not known to the receiver, except for the system of MO-RTT.
, histogram stretching is done with respect to Rayleigh distribution
Weibull Rayleigh distribution: Theory and applications.
For an ideal narrowband process, [f.sub.s](S) can be approximated by the Rayleigh distribution [21]; the analytical expression is given as
The Nakagami-m distribution is generally assumed to be a more general model, which would approximate Rice distribution when m > 1, Rayleigh distribution for m = 1, and fading more severe than Rayleigh when m < 1 [20].
Two kinds of statistic models including single distributions [3-5], such as the K distribution (K), Rayleigh distribution (RA), Rician distribution (RI), and Nakagami distribution, as well as compound distributions [6-9], such as the homodyned K distribution (HK), generalized K distribution, Rician inverse Gaussian distribution (RilG), Nakagami-generalized inverse Gaussian distribution (NGIGD), have been investigated for analyzing the statistical properties of the ultrasonic-echoed envelope data.
Wu, Lee and Hou (2007) explored the maximum likelihood estimation of life performance under Rayleigh distribution, and developed a test procedure for evaluating the performance of the product.