Moments

Compact shape summaries for I/O distributions - and explicit verdicts for when moments are the wrong tool. A tool I’ve been thinking about for fifteen years Some time around 2011, I started wondering whether you could characterize the shape of an I/O latency distribution - disk, filesystem, any streaming measurement - using only its first few moments, computed online, in kernel space where memory is expensive. Every PhD mathematician I asked told me some variant of “no, you can’t reconstruct a distribution from a finite number of moments; the problem is ill-posed.” They were answering a different question than the one I was asking. It took me most of fifteen years to articulate which question I actually had, and why their objection, though correct, did not apply to it. ...