5
$\begingroup$

Say I have height measurements of Earth's population expressed with a precision of integer centimetres. Height-in-cm Number-of-people 136 154934 137 158059 138 170372 139 220385 ...

In terms for this example that uses frequency weights, is there a numerical method to calculate q-tiles from a data set weighted by the cardinality of its entries?

More generally, how do I find the percentile p (or quantile q) from a weighted dataset that uses weights of any kind, e.g. frequency, sampling, IPTW, IPSW, etc.?

Is there a formula, such as something that I could implement in R, other than expanding this into a pseudo-dataset with ten billion values?

$\endgroup$
3
$\begingroup$

To solve for quantile $q$ in a weighted set of ordered observations $x_1, x_2, \ldots$:

Let $W$ be the sum of the weights.

Let $w_1, w_2, \ldots$ equal the observation weights ordered by the ranks of the observations.

Find the largest $k$ such that $w_1+w_2+\ldots+w_k \leq Wq$.

Then $x_k$ is your estimate for the $q$th quantile.

Notice $x_k$ estimates a range of quantiles, just like you would see if you created an expanded dataset replicating observations repeatedly based on their weights.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.