Talk:Percentile

Replacing WP

I replaced the WP import by a new article, and added an example (test results) previously inserted by Anh Nguyen (3rd revision, 10:11, 8 November 2006). Peter Schmitt 16:03, 23 November 2009 (UTC)

Not quite so

The implication

$P(\omega =x)>0\Rightarrow P(\omega \leq x)>{k \over 100}{\textrm {\ \ and\ \ }}P(\omega \geq x)>1-{k \over 100}$

is not always true; when k is at the left endpoint of the relevant interval, the first inequality is not strict; and when k is at the right endpoint of the relevant interval, the second inequality is not strict. In addition, I did not understand from the article, is k assumed to be integral, or not? If it is then these non-strict inequalities become more rare cases, but still possible. Boris Tsirelson 19:11, 26 November 2009 (UTC)

Thank you for spotting the p's. I changed from p to k and forgot them.

Yes, I think that percentiles are used for integer k. I am no statistician, so I cannot be absolutly sure. But I have two reasons to assume that integer values are the usual case (though everybody who understands them will understand arbitrary values):

They are usually called "k-th percentile.

For general probabilities there is the quantile.

And, yes, I overlooked the special case in the inequality. It should be "or" instead of "and".

Peter Schmitt 00:57, 27 November 2009 (UTC)

Another remark. It is written correctly "...in a population (or a sample)", but afterwards, all formulas are written in terms of probabilities, not frequencies. It would be cumbersome to write each formula in two forms. However, it could be explained to the reader that each formula has two, or even three, interpretations: (a) probabilities are given by a "theoretical" (often, continuous) distribution; (b) probabilities are frequencies in a finite population, and correspond to a random choice of one element from the population; (c) probabilities are frequencies in a sample, and correspond to a random choice of one element from the sample, which is related to bootstrap (resampling). Boris Tsirelson 10:13, 27 November 2009 (UTC)