Dear people,
OK, everyone, you win! Here is a summary of the Rayleigh Distribution
information I received. I’ve not yet had time to dig through the
references, but I'm sure multiples of them will work. I have not been
able to digest any of this, sorry. Well, at least one person assured me
I spelled the name right :)
What _is_ the Rayleigh Distribution?
Rayleigh distribution: "used mainly in engineering applications to
denote a special form of the Weibull distribution [with beta=2]. It
arises as the distribution of the miss distances from the target when
the coordinates of the point of impact have the circular normal
distribution with the center as its target."
It's black body radiation distribution if energy is continuous not
quantized, the one overturned by Planck.
Most decent texts on the Gamma or Weibull will mention this
Density , f(x)=(x/b^2)*exp(-x^2/(2b^2))
Cum. Distn, F(x)=1-exp(-x^2/(2b^2)) , b>0, x>0
mean b*sqrt(pi/2)
mode b
variance (2-pi/2)*b^2
When b = 1 it becomes a Chi-squared distribution with 2 d.f.
One may include a displacement factor, a, in there:
F(x)=1-exp-[(x-a)/b]^2 for x>a
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Where to find it?
The references - most are books, the next to last is a web site, and the
last is a paper. Otherwise, in author order:
Author
Title
Publisher Year
Bury, Karl V Statistical Models in Applied Science Wiley.
1975
Evans, Hastings and Peacock Statistical Distributions Second ed., (p
134) Wiley, New York, 1993
Freund and Williams Dictionary and Basic Outline of Statistics,
Dover
Goodman, J. W., Statistical Optics John Wiley and Sons, New
York, 1985
Johnson, Kotz and Balakrishnan compendia
Johnson, N. L., & Kotz, S. Continuous distributions in
statistics.(Vol. 2). Continuous Univariate Distributions, Vol. I.
Boston: Houghton Mifflin Co. 1 970
Marriott F.H.C., A dictionary of statistical terms, 5th Ed
Longman (1999 or 1990)
Cambridge Dictionary of Statistics
Best Fit manual Palisade, www.palisade.com
Tuthill, T. A., Sperry, R. H., and Parker, K. J. Deviation from
Rayleigh statistics in ultrasonic speckle Ultrasonic Imaging 10,
81--90 1988
-------------------
Who knows about it?
Many thanks to the following who provided more than I thought possible:
Dietrich Alte, Don W Brown, Nick Cox, Joe Haas, Tony Johnson, Miland
Joshi, Diana Kornbrot, Peter M Lee, Roger Owen, Dave Stewardson.
Apologies to any I missed.
Gratefully,
Jay
--
Jay Warner
Principal Scientist
Warner Consulting, Inc.
4444 North Green Bay Road
Racine, WI 53404-1216
USA
Ph: (262) 634-9100
FAX: (262) 681-1133
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web: http://www.a2q.com
The A2Q Method (tm). What do you want to improve today?
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