I came across this term, probability of correct selection (pcs) while going through this paper. home.iitk.ac.in/~kundu/paper140.pdf I've googled a lot but I don't seem to find an authoritative explanation. Could someone here please explain to me what the term means, especially in the context of choosing the best distribution (that fits a univariate lifetime dataset) among a set of pdfs(probability distributions)?

In this link ecommons.cornell.edu/bitstream/handle/1813/32947/BU-842-M.Revised.pdf?sequence=1, it is kind of apparent that (but not mentioned explicitly) pcs is 'selecting the best of k populations'. If it is so, can someone explain it to me in simpler terms?

The term 'probability of correct selection' literally means 'the probability of choosing the correct item'. Is that it?

I've tried to make this question as specific as possible. Please go through it completely before collapsing it as a subjective question(it is not).

If anyone can't access those pdf files, tell me.

The first link is a paper on a method for choosing a distribution (among log-normal, weibull and generalized exponential distributions) that fits a given sample data. The author mentions 'probability of correct selection'(pcs). I didn't understand exactly what that term meant so I asked the question here. What exactly does that term mean? 'Probability of correct selection' That's the crux of this question.

The second paper is one of the papers I found when googling the term. It's the only paper that's free and the rest, I have to buy (I can't afford them). The paper doesn't explain what the term is, but goes on to describe a method to estimate it (pcs).

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    $\begingroup$ Subjectivity is not a problem: but understandability is. Questions must stand on their own without relying on links to other sites to make them comprehensible. Could you therefore please summarize the context so that readers can follow your question without having to leave this site? $\endgroup$
    – whuber
    Jan 3 '16 at 14:22
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    $\begingroup$ @whuber Thank you for going through. Those links are optional and they aren't needed to answer the question. I'll try to be even more clear. $\endgroup$ Jan 3 '16 at 15:28

The second paper refers to the socalled "subset selection problem", a decision-theory formulation which have been much studied theoretically but semingly not much applied in practice. That problem is in the context of one-way anova with very many groups (maybe hundreds, think of the problem of selecting a high-yield variety).

The goal is to select the group with the highest mean, and the proposed method is to select a subset of the groups such that the probability that this group contains the group with the highest mean is guaranteed to be high, say for example 0.95. That probability is the PCS, probability of the correct selection.


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