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I noticed that different notations are used to denote the quantile function of probability distributions. The most common ones are ${\displaystyle Q(p)}$ (e.g. Tukey lambda distribution), ${\displaystyle Q(u)}$ (e.g. Dagum distribution), ${\displaystyle F^{-1}(\cdot )}$ (e.g. Kumaraswamy distribution), and ${\displaystyle x(F)}$ Laplace distribution. In other cases, the quantile function is redubbed as "random variate generation", and described as a transformation of a standard uniform random variable (rv), i.e. ${\displaystyle U\mapsto X}$ (e.g. Burr Type XII distribution).

Although I realize that this is similarly the case in the literature, I believe that arbitrarily inconsistent notation like this, can be very confusing to readers, especially newcomers. But unlike the published literature, here, the notation can be made consistent.

I don't have a strong preference myself, but I (usually) prefer ${\displaystyle x(F)}$ over ${\displaystyle F^{-1}(\cdot )}$ nowadays, since both ${\displaystyle Q(\cdot )}$ and ${\displaystyle F^{-1}(\cdot )}$ have no standard for the name of the parameter (I've seen ${\displaystyle p}$, ${\displaystyle q}$, ${\displaystyle u}$ and ${\displaystyle y}$ used in different places). I can also see that standard uniform transformation notation, e.g. ${\displaystyle X=-\log(1-U)}$ for the standard exponential distribution, could be a good choice, but only if it is described as being the "quantile function", and not only "random variate generation". jorenham (talk) 14:26, 14 December 2023 (UTC)[reply]

If we were going to try to standardise, I would prefer Q(u), particularly because it leads naturally to q(u) for the density quantile function. But note also that adopting a standard on Wikipedia would make it inconsistent with the way the quantile function is usually presented in the literature for some distributions. Newystats (talk) 02:34, 15 December 2023 (UTC)[reply]

Coupling the QF notation with that of the QDF makes sense to me.

I guess that notational inconsistency with the literature is inevitable. I even stumbled accross a ${\displaystyle G(p)}$ today (C.L. Mallows, '73).

Perhaps it's a good idea to explicitly list the common QF notations on the quantile function page? jorenham (talk) 02:54, 15 December 2023 (UTC)[reply]

I see some statistics software (e.g. Minitab) has an importance of mid-importance, but there's nothing for R, which I don't think reflects the importance R does have. Drkirkby (talk) 15:43, 3 February 2024 (UTC)[reply]

The article John H. Wolfe has gone through a PROD, but still has issues as it is based on one secondary textbook claim that his work on model-based clustering matters. It was created directly by a novice editor (Stat3472 33 edits). The article model-based clustering supports him as the inventor, but whether this is big enough for notability is unclear. Comments on the talk page please, perhaps better than AfD. Ldm1954 (talk) 09:56, 2 March 2024 (UTC)[reply]