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Talk:Noncentral t-distribution

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I can't figure out why the is rendering as Roman, rather than italic in this article. Compare to, say, Variance, but there it renders as PNG rather than HTML. And I don't think logging in with special preferences is a solution. — DIV (128.250.204.118 06:04, 18 March 2007 (UTC))[reply]

I agree that an italic mu would look better. I wish I knew how to make that appear. Steve8675309 00:29, 20 March 2007 (UTC)[reply]
This can be solved by placing \,\! at the end of each formula, as specified at MetaWikiPedia:Help:Formula#Forced_PNG_rendering. --128.250.5.248 (talk) 04:56, 12 August 2009 (UTC)[reply]

I think this description of the noncentral t-distribution is incomplete and overly confusing. A scale parameter is generally included and the density can be written much more succinctly. Jurgen (talk) 20:06, 4 May 2010 (UTC)[reply]

I am puzzled by the representation of the first form of the CDF. It specifies that when (x < 0) the recursive part of the function---~F()---operates on the reversed sign of x: but ~F() is utterly insensitive to the sign of x, since x only appears in squared terms (i.e. in y). So why bother to assert that the sign of x changes? mu changes sign, yes, but not x. Lexy-lou (talk) 16:14, 20 April 2014 (UTC)[reply]

In Section 1.2.1 Differential equation, the sign of the first derivative of the PDF at zero seems wrong. It says that the first derivative has the opposite sign of the non-centrality parameter ($\mu$), and from the plots of the PDF in the same article, and from general knowledge, when the non-centrality parameter is positive the PDF is increasing at zero. — Preceding unsigned comment added by Niausnil (talkcontribs) 13:35, 29 January 2015 (UTC)[reply]

Mode as a function of noncentrality parameter

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The subsection Noncentral t-distribution#Mode currently says

Moreover, the negative of the mode is exactly the mode for a noncentral t-distribution with the same number of degrees of freedom ν but noncentrality parameter −μ.
The mode is strictly increasing with μ when μ > 0 and strictly decreasing with μ when μ < 0.

These are mutually contradictory when μ < 0. The last part of the last sentence says that when μ is negative and increases toward 0, the mode goes in the opposite direction (away from 0). That conflicts with the first quoted sentence, which implies that the μ > 0 and μ < 0 cases both have the mode going in the same direction as μ.

Unless I hear an objection, I’ll change the last sentence to The mode is strictly increasing with μ. Loraof (talk) 20:07, 18 June 2018 (UTC)[reply]

Done. Loraof (talk) 18:03, 20 June 2018 (UTC)[reply]

Mode as a function of noncentrality parameter

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The subsection Noncentral t-distribution#Mode gives a lower and an upper bound to the mode:

.

Then it says:


"In the limit, when μ → 0, the mode is approximated by"


However this aproximation is worse (by worse I mean lower) than the lower bound: .

The article[1] from where this was taken doesn't compare the result it obtained for the μ → 0 approximation with the bounds it provided. Does anyone know why the lower bound would not be a better approximation than the currently one?

Zaphodxvii (talk) 03:03, 31 December 2020 (UTC)[reply]

Construction of a noncentral t-random variable

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In the definition of the noncentral -distribution, it defines as a normal random variable with mean and unit variance. If this variable already has mean , then the construction of a noncentral -random variable does not need . — Preceding unsigned comment added by Jourdy345 (talkcontribs) 18:05, 27 May 2022 (UTC)[reply]

  1. ^ van Aubel, A; Gawronski, W (2003). "Analytic properties of noncentral distributions". Applied Mathematics and Computation. 141: 3–12. doi:10.1016/S0096-3003(02)00316-8.