Perturbation function

The following discussion is an archived discussion of the DYK nomination of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Allen3 ^talk 20:09, 31 October 2011 (UTC)

Log-Cauchy distribution

Template:DYK nompage links Template:*mp... that the log-Cauchy distribution is a probability distribution without a finite mean?

• ALT1:... that the log-Cauchy distribution is a probability distribution without any finite non-trivial moments?
• Reviewed: Finners Quinlan

Created/expanded by Rlendog (talk). Self nom at 16:01, 19 October 2011 (UTC)

• I do not understand this hook. I have gone into the extra links to articles and attempted to research what this means. I still do not understand this hook. Is there an alternative which would give a simpler explanation for those who are mathematically challenged?

Other than this the article looks good. No plagarism that I can see and well sourced with adequate text. Just...confused. The whole thing is confusing. Help please! Panyd^{The muffin is not subtle} 14:49, 28 October 2011 (UTC)

The hook is about that if you try to calculate the average of this distribution, the result is infinite. Or some would say that it is undefined. But it is not a finite number, as most probability distributions produce. But maybe a less technical hook would be:

ALT2:... that the log-Cauchy distribution has been proposed as a model for the progression of the HIV virus? Rlendog (talk) 20:20, 28 October 2011 (UTC)

I like that! Appears to be backed by sources (although perhaps someone with a little more understanding of these things should double-check). I'd say with Alt2 that this is good to go! Panyd^{The muffin is not subtle} 21:17, 28 October 2011 (UTC)

The table of contents in the source's free Amazon preview seems to confirm AGF. It wasn't obvious to me from the hook that it's talking about rate of progression within an individual rather than rate of spread among a population. "HIV virus" is redundant, as the V stands for virus. In the article subsection on the PDF you refer to $\gamma$; do you mean $\mu$? Lagrange613 08:31, 30 October 2011 (UTC)

Thanks. I am not sure it is necessary for a hook to specify that it is for individuals rather than the population, since the idea is to hook people into reading the article to find out the details. But it probably doesn't hurt to include it. How about:

ALT3: ... that the log-Cauchy distribution has been proposed as a model for the progression of HIV in individuals?

I actually think that the reference to the PDF you caught should be $\sigma$ instead of $\gamma$, at least based on the source, so I edited the article accordingly. Rlendog (talk) 14:34, 31 October 2011 (UTC)

Good to go on all review criteria. AGF on the offline source, but like I said above it's a robust AGF. Thanks for addressing my nitpicks. Lagrange613 16:12, 31 October 2011 (UTC)