Talk:Lévy distribution

Non-negative?

The intro says that Levy distribution is defined on a non-negative random variable (x). But if μ < 0, then x can be negative since x belongs to [μ, infinity). — Preceding unsigned comment added by 128.40.79.203 (talk) 14:07, 5 December 2013 (UTC)

Nomenclature

Why is this sometimes called the Mandelbrot-Levy distribution? Did Mandelbrot, who has an air for publicity, simply append his name to something he studied? Or did he contribute something in this field? User:raylopez99 07:45, 12 September 2006 (UTC)

I think you are half right. The serious stats references are to one B. Mandelbrot writing in the 60s, which I assume is the same fellow back when he was doing real work instead of seeking the limelight with overblown fractal nonsense. So there you might be incorrect and the hyphen is "deserved" - however, the way these things go, his later notoriety may have played a role in assigning the accolade to him. 2A01:CB0C:761:5B00:8160:74EE:9BA7:B262 (talk) 08:12, 31 March 2024 (UTC)

Significance

Can someone explain the significance of this? I mean, right now the page is nothing more than a definition, a not very informative comparison to other functions, and a ton of mathematical speak that anyone who's not a mathematician will understand. What is this function typically used for? What does it typically graph? etc. 66.189.210.56 06:06, 17 May 2007 (UTC)

Not very useful

This article is little more than showing off while explaining nothing. No one without a strong background in statistics can extract any meaning at all from it.

I agree. What the h*ll is an undefined excess kurtosis, anyway? How can you cook it? :D 83.59.187.193 13:17, 17 May 2007 (UTC)

This distribution was in the news this week in connection to an experiment about the flight patterns of fruit flies, http://www.foxnews.com/story/0,2933,272938,00.html

I had hoped to find an explanation of what significance this distribution has, but despite having taken 3 semesters of calculus in college I can't make heads nor tails out of this article.

The article is a pretty standard description of a probability distribution, offering the formulas for the common quantities of interest. More information is available at Lévy skew alpha-stable distribution, but there doesn't seem to be a really good definition of the utility of this distribution on wikipedia. You might also want to look at Lévy flight. digfarenough (talk) 20:56, 19 May 2007 (UTC)

I agree that this is an unusually unhelpful article that badly needs an introduction. Levy distribution crops up in all sorts of places (search flights of fruitflies and honeybees, for example) & the information here should be able to help people from those disciplines. At the moment it doesn't. Cooke 21:13, 11 November 2007 (UTC)

Instead of complaining, why don't you become an editor? I put together most of this article simply because it was one of the analytically expressible cases of the more general Lévy skew alpha-stable distribution, so I am quite sure it is useful, but I never researched specifically how it was useful. Stop complaining and start editing! PAR 21:47, 11 November 2007 (UTC)

Mathematical Mistake

The Characteristic function described in the text and one in the table that summarize the properties of the distribution are different. One of the two must be wrong. Could someone tell us which one is the right one?

No, they agree. Note that the one in the text includes a shift parameter μ which is not included in the function in the table. Since the function in the table says the support is [0,infinity), substitute μ=0 in the text function, which yields the function from the table. digfarenough (talk) 18:42, 20 July 2007 (UTC)

Link to heavy tail

The link to heavy-tails goes to long-rage dependency. Would it not be better to send it to the article on heavy-tailed distributions. Although that article is more mathematical, it will asist the reader who wants to know more. PoochieR (talk) 09:34, 24 January 2008 (UTC)

Utterly incoherant

This reads like one of the Bogdanov twins' lesser-known works. I wager that the only folk capable of making sense of this article are already completely knowledgable as to the subject covered. Would it be at all possible to re-write this in such a way that would bring new insight to the previously unenlightened reader? --Badger Drink (talk) 23:31, 10 August 2008 (UTC)

Not quite so bad

The article did help me when teaching the course "Brownian motion". Well, I was of course knowledgeable, but not completely! Also my students were able to look here. Boris Tsirelson (talk) 20:18, 25 August 2008 (UTC)

picture over formula

Something is wrong with the last edit by Melcombe: on my screen, the picture (Probability density function for the Lévy distribution) hides a part of the previous text and formula. Boris Tsirelson (talk) 19:11, 29 January 2009 (UTC)

Oops... It is not. Somehow the bad effect was temporary. Sorry for the fuss. Boris Tsirelson (talk) 19:15, 29 January 2009 (UTC)

Fruit fly flight

The article claims that "It is claimed that fruit flies follow a form of the distribution to find food." Are we sure that the author of the referenced article wasn't confusing this particular distribution with a Levy process, which would yield a Levy alpha stable distribution, of which the Levy distribution that is the subject of this article is an example, but goes more generally by the name stable distribution? It seems very odd that this asymmetric distrubtion, rather than a symmetric stable distribution, would describe a fruit fly's flight pattern. I also wonder if the reference to financial modeling also is more a reference to the general stable distribution family, rather than this particular distribution. Rlendog (talk) 16:31, 28 July 2009 (UTC)

The biological stuff in this area seems to be talking about Lévy flight mostly (which I think is a type of Levy process), which is indeed not the same thing... The point is that the animals movements are modelled as a series of steps, taken in uniformly random directions, with lengths distributed according to an inverse power law. So yes that should lead to a stable distribution over time. The individual steps could be distributed as just about anything that has an inverse power law tail AFAIK, for example a Pareto distribution. The biological stuff would probably be better linked from the Lévy flight page rather than this one. Couldn't comment on financial modelling though, but it sounds like you're probably right. 188.221.54.25 (talk) 11:09, 2 June 2010 (UTC)

maximum

what are the maxima for c=0.5, c=1, etc. --46.115.87.234 (talk) 12:26, 19 October 2013 (UTC)

"The time of hitting a single point, at distance α {\displaystyle \alpha } from the starting point, by the Brownian motion has the Lévy distribution with c = α 2 {\displaystyle c=\alpha ^{2}}"

Brownian motion in 2D? 2A01:CB0C:761:5B00:8160:74EE:9BA7:B262 (talk) 08:05, 31 March 2024 (UTC)