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Topic: Rayleigh distribution

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Rayleigh fading

Probability distribution

Uniform distribution (continuous)

Laplace distribution

Normal distribution

Exponential distribution

Gamma distribution

Exponential family

Erlang distribution

Lord Rayleigh

Weibull distribution

Gumbel distribution

Cumulative distribution function

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	RR-4121 : Modelling SAR with a Generalisation of the Rayleigh Distribution
		some alternative distributions have been suggested such as weibull and log-normal distributions, however, in most of the cases these models are empirical, not derived with the consideration of underlying physical conditions and therefore are case specific.
		we also derive novel methods for the estimation of the heavy-tailed rayleigh distribution parameter- s based on negative fractional-order statistics for model fitting.
		Nous présentons également de nouvelles mèthodes d'estimation des paramètres d'une distribution de Rayleigh à queue lourde fondées sur des statistiques d'ordre fractionnaire négatif.
	www.inria.fr /rrrt/rr-4121.html (556 words)

	Rayleigh distribution - Wikipedia, the free encyclopedia
		The Chi distribution is a generalization of the Rayleigh distribution.
		The Rice distribution is a generalization of the Rayleigh distribution.
		The Weibull distribution is a generalization of the Rayleigh distribution.
	en.wikipedia.org /wiki/Rayleigh_distribution (300 words)

	Rayleigh Distribution
		The distribution is used in physics where it is used in the study of various types or radiation, such as sound and light and in signal processing.
		Where the Rayleigh distribution is a poor model for a given location, it may be appropriate to fit the data to a Weibull distribution.
		This is effectively changing the shape factor from an independent variable to a dependent one (the Rayleigh distribution is a Weibull one with the shape factor set to two).
	www.brighton-webs.co.uk /distributions/rayleigh.asp (662 words)

	Springer Online Reference Works
		the Rayleigh distribution coincides with the distribution of the square root of a random variable which has the  "chi-squared" ; distribution with two degrees of freedom.
		In other words, a Rayleigh distribution can be interpreted as the distribution of the length of a vector in a plane Cartesian coordinate system, the coordinates of which are independent and have the normal distribution with parameters 0 and
		It was first considered by Lord Rayleigh in 1880 as the distribution of the amplitude resulting from the addition of harmonic oscillations.
	eom.springer.de /r/r077730.htm (216 words)

	week02notes
		The distribution of area under the normal distribution is such that 68% of the observations fall within 1 standard deviation above and below the mean, 95.4% fall within 2 standard deviations and 99.73% fall within 3 standard deviations of the mean.
		One interesting property of the Rayleigh distribution is that the log of the Rayleigh distribution is approximately normal in distribution.
		This distribution is the basis for statistical hypothesis testing of sample population means using the t-test.
	www.personal.kent.edu /~jortiz/earthstats/topic02notes.html (3139 words)

	Distribution Fitting
		To determine this underlying distribution, it is common to fit the observed distribution to a theoretical distribution by comparing the frequencies observed in the data to the expected frequencies of the theoretical distribution (i.e., a Chi-square goodness of fit test).
		The major distributions that have been proposed for modeling survival or failure times are the exponential (and linear exponential) distribution, the Weibull distribution of extreme events, and the Gompertz distribution.
		The beta distribution arises from a transformation of the F distribution and is typically used to model the distribution of order statistics.
	www.statsoft.com /textbook/stdisfit.html (1769 words)

	Weibull distribution online. Including the exponential and Rayleigh distribution.
		The exponential distribution (used to study waiting times) is a special case of the Weibull distribution with alpha=1, mean=beta and lambda(the hazard rate)=1/beta.
		Sometimes the distribution is used as an alternative to the normal distribution in the case of skewed data.
		Although the distribution is the most used extreme value distribution there are other extreme value distributions describing the limiting distribution for the smallest or largest values drawn from particular distributions.
	home.clara.net /sisa/weibhlp.htm (647 words)

	Rayleigh Explanation (Site not responding. Last check: 2007-10-23)
		I keep adjusting the input wind speed to the Raleigh distribution until the effective velocity of the Rayleigh distribution matches the effective velocity that the wind turbine actually experienced.
		If I report the average wind speed of 13.25 mph, and a Rayleigh wind speed of 13.6 mph, that says that my 13.25 mph winds had the same energy as a 13.6 mph average wind with a Rayleigh distribution.
		The significance of this is that manufacturers assume a Rayleigh distribution in estimating the energy a turbine would produce given a certain wind speed.
	www.ndsu.nodak.edu /ndsu/klemen/Rayleigh_Explanation.htm (342 words)

	Mariners Weather Log Vol. 49, No. 2, August 2005
		This distribution is quite good at describing phenomena in which most elements in a group are clustered near an average value with an equal number of elements being greater and less than this average value.
		Since the Rayleigh distribution actually goes to infinity to the right of its peak, a wave is theoretically not bounded by a limiting height.
		Theoretical Rayleigh distribution of the wave heights at Buoy 42040 at 8:00 p.m.
	www.vos.noaa.gov /MWL/aug_05/nws.shtml (1740 words)

	PlanetMath: Weibull random variable (Site not responding. Last check: 2007-10-23)
		The resulting distribution is called the standard Weibull, or Rayleigh distribution:
		The Weibull distribution is often used to model reliability or lifetime of products such as light bulbs.
		Cross-references: exponential distribution, iff, mode, median, gamma function, distribution, transformation, probability density function
	planetmath.org /encyclopedia/RayleighDistribution.html (127 words)

	Distributions (Site not responding. Last check: 2007-10-23)
		The exponential distribution is a special case of the gamma distribution where a=1 and B = 1/lambda.
		The probability distribution of a narrow band noise process n(t) was formulated by Rice in papers published in the Bell Laboratories Journal, 1944 and 1945.
		The Rician probability density function is derived as for the Rayleigh distribution by considering the in-phase and quadrature components.
	local.wasp.uwa.edu.au /~pbourke/other/distributions/index.html (901 words)

	Springer Online Reference Works
		In other words, a Maxwell distribution can be obtained as the distribution of the length of a random vector whose Cartesian coordinates in three-dimensional space are independent and normally distributed with parameters
		The Maxwell distribution is widely known as the velocity distribution of particles in statistical mechanics and physics.
		The distribution was first defined by J.C. Maxwell (1859) as the solution of the problem on the distribution of velocities of molecules in an ideal gas.
	eom.springer.de /m/m063130.htm (192 words)

	RAYCDF
		The Rayleigh distribution is a special case of the
		It is also a special case of the Weibull distribution with shape parameter = 2 and scale parameter =
		The standard Rayleigh distribution is the case with
	www.itl.nist.gov /div898/software/dataplot/refman2/auxillar/raycdf.htm (189 words)

	UNIFORM DISTRIBUTION
		The algorithm for generating gamma distributed random variables proposed by Cheng in 1977 is given below.
		The transform method is used to generate Laplacian distributed random variates.
		An example of a Laplacian distributed random variable is human voice.
	www.cse.msu.edu /~nandakum/nrg/Tms/student/student.htm (598 words)

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