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| <section id="quantiles-sketches"> |
| <h1>Quantiles Sketches<a class="headerlink" href="#quantiles-sketches" title="Link to this heading"></a></h1> |
| <p>Quantile estimation is useful for understanding the distribution of data values in a stream. The sketches currently |
| in the library are designed to answer queries about the <cite>rank</cite> of an item in the stream of items. That is, when |
| applying a global ordering on all the items, what is the portion of items seen so far that are less than (alternatively, |
| less-than-or-equal-to) the given item. Using straightforward logic, they can also estimate the item at a given rank |
| in the stream.</p> |
| <p>These sketches may be used to compute approximate histograms, Probability Mass Functions (PMFs), or |
| Cumulative Distribution Functions (CDFs).</p> |
| <p>The library provides four types of quantiles sketches, three of which have generic items as well as versions |
| specific to a given numeric type (e.g. integer or floating point values). Those three types provide error |
| bounds on rank estimation with proven probabilistic error distributions. t-digest is a heuristic-based sketch |
| that works only on numeric data, and while the error properties are not guaranteed, the sketch typically |
| does a good job with small storage.</p> |
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| <div><ul class="simple"> |
| <li><p>KLL: Provides uniform rank estimation error over the entire range.</p></li> |
| <li><p>REQ: Provides relative rank error estimates, which decreases approaching either the high or low end values.</p></li> |
| <li><p>t-digest: Relative rank error estimates, heuristic-based without guarantees but quite compact with generally very good error properties.</p></li> |
| <li><p>Classic quantiles: Largely deprecated in favor of KLL, also provides uniform rank estimation error. Included largely for backwards compatibility with historic data.</p></li> |
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| <li class="toctree-l1"><a class="reference internal" href="quantiles_depr.html">Quantiles Sketch (Deprecated)</a></li> |
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