Hi! I am working on a paper about calculation quantiles in a fast way. It is easy to calculate different sets of quantiles, like q25, q50, q75   or  the 9 quantiles (q1, q5, q10, q25, q50, q75, q90, q95, q99). And also the full set of 99 quantiles (q1, q2, q3,,,,q99). My first question:   How many quantiles and which are of interest to the user? How are quantile values like q1, q5, q10 (and q90, q95, q99) used? (Note: the step from 3 to 99 quantiles is almost without any cost.) My second question:  What accuracy is neeeded and wanted  and on what quantiles? Is the estimated Xp value (the quantile on the x-axis)  important   or  the p-value (on the CCDF, the percentage value on the y-axis,) of the estimated Xp-value?        Background: The calculated quantiles are usually more exact around the median, while q1, q5 and q95, q99 are less exact.        The median q50 and similar are more exact, since most values fall between q25 and q75, with a peak around q50. A small change (error) delta in q50 corresponds to a rather big change epsilon in the Calculated Cumulative Distribution Function (CCDF), since the CCDF curve is very steep around q50.         The calculations of q1, q5, q10 and q90, q95, q99 are less exact, since there are fewer data values at the extreme ends. A large change (error) delta in q1, q5, q10 (or q90, q95, q99) corresponds to a rather small change epsilon in the CCDF, since the CCDF curve is very flat at the extreme ends. All calculations are made on Calculated Probability Distribution Function (CPDF) and CCDF, when trying to get information to describe the Experimental Distribution Function (ECDF).   I hope that you understand my questions!     /Br Anders ... View more