Talk:Rice distribution

message: Any comment about the cdf will be highly appreciated.
--Lucas Gallindo 18:34, 21 August 2007 (UTC)
replies: text: The cdf looks awesome, a bit like the one for the normal distribution. --WikiSlasher (talk) 07:48, 14 December 2007 (UTC)

message: This is clearly a very cumbersome distribution to work with, so it must have been imagined for a specific reason.  Could anyone explain a little what the thinking behind the distribution is?  Is it the distribution of something specific process (c.f. Poisson) or is it constructed to prove a point (c.f. Cauchy distribution or Cantor distribution). 83.244.153.18 (talk) 16:26, 30 July 2008 (UTC)
thread_title:  What is this distribution for? 

message: The CDF is given in terms of Q_1, with the note that
 Q_1 is the Marcum Q-Function
But this appears not to be described on Wikipedia. It is described on MathWorld, should a link be added within the CDF section of the sidebar, and/or within the references?
--Ged.R (talk) 14:45, 8 December 2008 (UTC)
replies: text: Yeah, it's probably a good idea at least until a Wikipedia article about it is written. I'd put it as an extra link in the sidebar. --WikiSlasher (talk) 15:46, 29 December 2008 (UTC)
thread_title:  Marcum Q-Function ref? 

message: Which is correct article title? The normal distribution is sometimes called the 'Gaussian', not the 'Gauss' so I think 'Rician' is more appropriate. -Roger (talk) 20:01, 1 April 2009 (UTC)
thread_title:  'Rice' or 'Rician'? 

message: The Wikipedia page Laguerre polynomials about Laguerre polynomials only gives definitions for L_n(x) for integer n. How is the definition for n=1/2 as used in the raw moment of the Rice distribution as proposed in this article?
Troelspedersen (talk) 11:31, 28 April 2010 (UTC)
thread_title:  Definition of the Laguere polynomial <math>L_{1/2}(x)</math> 

message: How is this inversion technique discovered? Could someone provide some guidance on this? Thanks.  —Preceding unsigned comment added by 68.246.18.196 (talk) 05:55, 14 May 2010 (UTC)
replies: text: Well, it is rather trivial. First notice that the distribution depends only on the value of the ratio θ = ν/σ. Then you see the formula for variance? If you divide it through by σ² and plug in the definition of the function L1/2 in terms of the Bessel functions (the formula is given in the “Moments” section), then you will obtain that the (normalized) variance is given by ξ(θ) expression. Then if you look at the expression for the mean and compare it with the expression for the variance, it all can be written as (Mean² + Var)/σ² = 2 + θ². Combined with the nonlinear equation that ξ(θ) = Var/σ² immediately gives you the formula that g(θ) = θ, where function g is as defined in the article.  // stpasha »  17:45, 14 May 2010 (UTC)

text: This “Koay technique” certainly looks nice and impressive and scientific-y, with all those special functions and fixed-point arguments and iterative schemes. But any statistician will tell you that this is not the “best” technique for this point. That is, there are methods which give more efficient and faster estimates. For example the one-step estimator in this case would be relatively simple (requires computation of special functions only once) and efficient. In particular, it will be as efficient as MLE and more efficient than the Koay method.  // stpasha »  06:46, 15 May 2010 (UTC)
thread_title:  The Koay inversion technique 

message: I am almost certain that in the limiting case where v >> sigma, the Rice distribution reduces to a Gaussian, since it is essentially the absolute value of a complex-valued gaussian random variable with non-zero mean.  — Preceding unsigned comment added by 199.46.245.230 (talk) 00:19, 13 June 2012 (UTC)
thread_title:  Limiting case