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:@[[User:Joe Gatt|Joe Gatt]] This edit and thread was created by me, I just hadn't logged in. Your edit was incorrect. I think you were confused by the notation - it's OK to have F(x) = int ^ x. What wouldn't be OK would be to have F(X) = int ^ X as a CDF definition (see [[Probability integral transform]]). Technically, X is a function of a probability space. Under certain restrictions, X(w) = x where w is in some original psp and x is in the support or range of the function X.
:As written, the CDF definition is back to being correct. [[User:Chjacamp|Chjacamp]] ([[User talk:Chjacamp|talk]]) 00:20, 24 November 2024 (UTC)
== Please clarify how area inequalities follow from diagram ==
The "Properties" section states the inequalities <math display="block">
x (1-F_X(x)) \leq \int_x^{\infty} t\,dF_X(t)
</math>
and
<math display="block">
x F_X(-x) \leq \int_{-\infty}^{-x} (-t)\,dF_X(t)
</math>
for a random variable <math>X</math> with a finite <math>L_1</math>-norm. These inequalities are straightforward to derive from the formula for the expected value of <math>X</math> using integration by parts. But the article claims that we can instead see why the inequalities are true from the included diagram by "consider[ing] the areas of the two red rectangles and their extensions to the right or left up to the graph of <math>F_X</math>". I don't see how these equalities follow from the diagram; please clarify. [[User:Ted.tem.parker|Ted.tem.parker]] ([[User talk:Ted.tem.parker|talk]]) 00:06, 24 March 2025 (UTC)
== Hatnote to pdf ==
There is [[Talk:Cumulative density function#RfC on redirect, disambig, article, or deletion|a discussion]] (RfC) on what to do with the page [[cumulative density function]]. One option is that it should redirect to this page. Some editors suggest that there should then be a hatnote here linking to [[probability density function]]. Please join the discussion! —[[User:St.nerol|St.Nerol]] ([[User talk:St.nerol|talk]], [[Special:Contributions/St.nerol|contribs]]) 16:59, 1 May 2025 (UTC)
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