|WikiProject Statistics||(Rated Start-class, High-importance)|
I know the distinction between strict and non-strict inequality doesn't matter for CONTINUOUS random variables, but it DOES matter for discrete ones, and there are situations where it's useful to use the survival function for discrete variables, and you will screw up if you use non-strict.
I'm sorry, but I can only assume that this is wrong. If we were to generate a discrete survival function from a sample set (say, Bob, Jill, and Fred), we would have to take into account every time period that each were alive. So, in this case, lets say we use decade intervals to generate our survival function. Then, we have that Bob died when he was in his 20's, Jill died when she was in her 50's, and then Fred died when he was in his teens. f(0 to 10) = 3 because they were all alive then, but f(<10 to 20) = 2 because Fred died, then f(<20 to 50) = 1 because that's when Bod died, and then f(<50 to inf) = 0 because then Jill died. Note, we have to take into account all times each was alive, thus the function must be monotone decreasing. 22.214.171.124 (talk) 06:06, 8 June 2011 (UTC)SomeGuyWhoApparentlyKnowsSomeMath
left continuous vs. right continuous
The distribution function is right continuous, so survivor function is left continuous. Jackzhp (talk) 20:55, 28 January 2011 (UTC) Not true. The definition of right-continuous is preserved under the map f(x) |-> 1-f(x). — Preceding unsigned comment added by 126.96.36.199 (talk) 13:30, 16 May 2013 (UTC)
Proposal to restore deleted material
Isambard Kingdom recently deleted material from the survival function article, with the justification that the material is too detailed. It may be helpful to consider the goals of a Wikipedia page.
- "The goal of a Wikipedia article is to create a comprehensive and neutrally written summary of existing mainstream knowledge about a topic."
A common criticism of Wikipedia statistics articles is that they are not comprehensible to non-statisticians. Here are examples from one of the survival analysis pages.
- "Please, somebody, take pity on those of us who need more fundamental understanding, and write an introduction to this subject that would be useful and graspable by anybody with the basic interest to look it up. That's how to make Wikipedia better; make it useful."
- "There should be a description of the assumptions needed for this model"
- "it doesn't describe any details about the model"
After the deletions by Kingdom, the article lacks many items that would be required for it to be considered comprehensive, including the following.
- The definition of the survival function is not sufficient to be informative for a reader not already familiar with survival functions and integral calculus.
- There is no explanation of how a survival function is calculated or estimated.
- There is no explanation of the relationship between density function, cumulative distribution function, and survival function.
- There is no explanation of the hazard rate, which is a key concept for understanding parametric survival functions. There is no explanation of the relationship between hazard rate and mean time to failure.
- There are no examples of survival functions for real data.
- There are no graphs of survival functions.
All these topics were covered in the material that was deleted. For these reasons, I think that most of the material that was deleted should be restored, and that a more nuanced editing to remove excess detail would be desirable.
If readers with more advanced knowledge, such as Kingdom, find the material too detailed and tedious, then one solution would be to move the introductory material to the end of the article. The material could be in a section with the title "Introduction to the survival function for the novice". In that way, readers who wish for a brief, mathematical, highly technical explanation can get that first, while readers who wish for a more comprehensible lay-oriented explanation can find it at the end. — Preceding unsigned comment added by Michaelg2015 (talk • contribs) 20:11, 14 January 2017 (UTC)