ghat | Reuse GitHub Actions workflows across repositories | BPM library

First of all, if you sum your column df$ghat, you'll see that it sums up to 100. So your 10th quantile should be >= 10 and your 90th >= 90.

After that, it seems like you are basically estimating the quantiles for grouped data. So the way you calculate it is a bit different than the usual way. You can see the formula in math is fun in a easily digestable format under "Estimating the Median from Grouped Data": https://www.mathsisfun.com/data/frequency-grouped-mean-median-mode.html.

I could explain it in my own words about what they talk in the website, but it's so clear in there I don't want to ruin it really. To calculate the 10th and 90th quantile, you can basically convert their formula into respectively:

10th quantile

90th quantile

where (in bold the "conversion" of the variables in their post to your case):

• L is the lower class boundary of the group containing the quantile
• n is the sum of the density (in this case, 100)
• B is the cumulative density of the groups before the quantile group
• G is the density of the group
• w is the group width

Usually in integer groups, they place the lower bound and upper bound of the group in between the elements, which is also doable in your case. In case of the group with theta = 0.10, which is after theta = 0.09 and before theta = 0.11, the respective lower bound would be:

The width w mentioned in the formula can also be calculated, based on the boundaries of the group. Considering the previously mentioned example, the lower boundaries of theta 0.10 and 0.11 are respectively L(0.10) = 0.095 and L(0.11) = 0.105, so the width of the first group would be