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    <h1 class="heading"><a href="../index.html">
        <span>Presto 323 Documentation</span></a></h1>
    <h2 class="heading"><span>7.14. Aggregate Functions</span></h2>
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  <div class="section" id="aggregate-functions">
<h1>7.14. Aggregate Functions</h1>
<p>Aggregate functions operate on a set of values to compute a single result.</p>
<p>Except for <a class="reference internal" href="#count" title="count"><code class="xref py py-func docutils literal"><span class="pre">count()</span></code></a>, <a class="reference internal" href="#count_if" title="count_if"><code class="xref py py-func docutils literal"><span class="pre">count_if()</span></code></a>, <a class="reference internal" href="#max_by" title="max_by"><code class="xref py py-func docutils literal"><span class="pre">max_by()</span></code></a>, <a class="reference internal" href="#min_by" title="min_by"><code class="xref py py-func docutils literal"><span class="pre">min_by()</span></code></a> and
<a class="reference internal" href="#approx_distinct" title="approx_distinct"><code class="xref py py-func docutils literal"><span class="pre">approx_distinct()</span></code></a>, all of these aggregate functions ignore null values
and return null for no input rows or when all values are null. For example,
<a class="reference internal" href="#sum" title="sum"><code class="xref py py-func docutils literal"><span class="pre">sum()</span></code></a> returns null rather than zero and <a class="reference internal" href="#avg" title="avg"><code class="xref py py-func docutils literal"><span class="pre">avg()</span></code></a> does not include null
values in the count. The <code class="docutils literal"><span class="pre">coalesce</span></code> function can be used to convert null into
zero.</p>
<p>Some aggregate functions such as <a class="reference internal" href="#array_agg" title="array_agg"><code class="xref py py-func docutils literal"><span class="pre">array_agg()</span></code></a> produce different results
depending on the order of input values. This ordering can be specified by writing
an <a class="reference internal" href="../sql/select.html#order-by-clause"><span class="std std-ref">ORDER BY Clause</span></a> within the aggregate function:</p>
<div class="highlight-sql"><div class="highlight"><pre><span></span><span class="n">array_agg</span><span class="p">(</span><span class="n">x</span> <span class="k">ORDER</span> <span class="k">BY</span> <span class="n">y</span> <span class="k">DESC</span><span class="p">)</span>
<span class="n">array_agg</span><span class="p">(</span><span class="n">x</span> <span class="k">ORDER</span> <span class="k">BY</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
</pre></div>
</div>
<div class="section" id="general-aggregate-functions">
<h2>General Aggregate Functions</h2>
<dl class="function">
<dt id="arbitrary">
<code class="descname">arbitrary</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; [same as input]</dt>
<dd><p>Returns an arbitrary non-null value of <code class="docutils literal"><span class="pre">x</span></code>, if one exists.</p>
</dd></dl>

<dl class="function">
<dt id="array_agg">
<code class="descname">array_agg</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as input]&gt;</dt>
<dd><p>Returns an array created from the input <code class="docutils literal"><span class="pre">x</span></code> elements.</p>
</dd></dl>

<dl class="function">
<dt id="avg">
<code class="descname">avg</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the average (arithmetic mean) of all input values.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">avg</code><span class="sig-paren">(</span><em>time interval type</em><span class="sig-paren">)</span> &#x2192; time interval type</dt>
<dd><p>Returns the average interval length of all input values.</p>
</dd></dl>

<dl class="function">
<dt id="bool_and">
<code class="descname">bool_and</code><span class="sig-paren">(</span><em>boolean</em><span class="sig-paren">)</span> &#x2192; boolean</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">TRUE</span></code> if every input value is <code class="docutils literal"><span class="pre">TRUE</span></code>, otherwise <code class="docutils literal"><span class="pre">FALSE</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="bool_or">
<code class="descname">bool_or</code><span class="sig-paren">(</span><em>boolean</em><span class="sig-paren">)</span> &#x2192; boolean</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">TRUE</span></code> if any input value is <code class="docutils literal"><span class="pre">TRUE</span></code>, otherwise <code class="docutils literal"><span class="pre">FALSE</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="checksum">
<code class="descname">checksum</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; varbinary</dt>
<dd><p>Returns an order-insensitive checksum of the given values.</p>
</dd></dl>

<dl class="function">
<dt id="count">
<code class="descname">count</code><span class="sig-paren">(</span><em>*</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the number of input rows.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">count</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the number of non-null input values.</p>
</dd></dl>

<dl class="function">
<dt id="count_if">
<code class="descname">count_if</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the number of <code class="docutils literal"><span class="pre">TRUE</span></code> input values.
This function is equivalent to <code class="docutils literal"><span class="pre">count(CASE</span> <span class="pre">WHEN</span> <span class="pre">x</span> <span class="pre">THEN</span> <span class="pre">1</span> <span class="pre">END)</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="every">
<code class="descname">every</code><span class="sig-paren">(</span><em>boolean</em><span class="sig-paren">)</span> &#x2192; boolean</dt>
<dd><p>This is an alias for <a class="reference internal" href="#bool_and" title="bool_and"><code class="xref py py-func docutils literal"><span class="pre">bool_and()</span></code></a>.</p>
</dd></dl>

<dl class="function">
<dt id="geometric_mean">
<code class="descname">geometric_mean</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the geometric mean of all input values.</p>
</dd></dl>

<dl class="function">
<dt id="max_by">
<code class="descname">max_by</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span> &#x2192; [same as x]</dt>
<dd><p>Returns the value of <code class="docutils literal"><span class="pre">x</span></code> associated with the maximum value of <code class="docutils literal"><span class="pre">y</span></code> over all input values.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">max_by</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>n</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as x]&gt;</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">n</span></code> values of <code class="docutils literal"><span class="pre">x</span></code> associated with the <code class="docutils literal"><span class="pre">n</span></code> largest of all input values of <code class="docutils literal"><span class="pre">y</span></code>
in descending order of <code class="docutils literal"><span class="pre">y</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="min_by">
<code class="descname">min_by</code><span class="sig-paren">(</span><em>x</em>, <em>y</em><span class="sig-paren">)</span> &#x2192; [same as x]</dt>
<dd><p>Returns the value of <code class="docutils literal"><span class="pre">x</span></code> associated with the minimum value of <code class="docutils literal"><span class="pre">y</span></code> over all input values.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">min_by</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>n</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as x]&gt;</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">n</span></code> values of <code class="docutils literal"><span class="pre">x</span></code> associated with the <code class="docutils literal"><span class="pre">n</span></code> smallest of all input values of <code class="docutils literal"><span class="pre">y</span></code>
in ascending order of <code class="docutils literal"><span class="pre">y</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="max">
<code class="descname">max</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; [same as input]</dt>
<dd><p>Returns the maximum value of all input values.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">max</code><span class="sig-paren">(</span><em>x</em>, <em>n</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as x]&gt;</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">n</span></code> largest values of all input values of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="min">
<code class="descname">min</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; [same as input]</dt>
<dd><p>Returns the minimum value of all input values.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">min</code><span class="sig-paren">(</span><em>x</em>, <em>n</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as x]&gt;</dt>
<dd><p>Returns <code class="docutils literal"><span class="pre">n</span></code> smallest values of all input values of <code class="docutils literal"><span class="pre">x</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="sum">
<code class="descname">sum</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; [same as input]</dt>
<dd><p>Returns the sum of all input values.</p>
</dd></dl>

</div>
<div class="section" id="bitwise-aggregate-functions">
<h2>Bitwise Aggregate Functions</h2>
<dl class="function">
<dt id="bitwise_and_agg">
<code class="descname">bitwise_and_agg</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the bitwise AND of all input values in 2’s complement representation.</p>
</dd></dl>

<dl class="function">
<dt id="bitwise_or_agg">
<code class="descname">bitwise_or_agg</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the bitwise OR of all input values in 2’s complement representation.</p>
</dd></dl>

</div>
<div class="section" id="map-aggregate-functions">
<h2>Map Aggregate Functions</h2>
<dl class="function">
<dt id="histogram">
<code class="descname">histogram</code><span class="sig-paren">(</span><em>x) -&gt; map(K</em>, <em>bigint</em><span class="sig-paren">)</span></dt>
<dd><p>Returns a map containing the count of the number of times each input value occurs.</p>
</dd></dl>

<dl class="function">
<dt id="map_agg">
<code class="descname">map_agg</code><span class="sig-paren">(</span><em>key</em>, <em>value) -&gt; map(K</em>, <em>V</em><span class="sig-paren">)</span></dt>
<dd><p>Returns a map created from the input <code class="docutils literal"><span class="pre">key</span></code> / <code class="docutils literal"><span class="pre">value</span></code> pairs.</p>
</dd></dl>

<dl class="function">
<dt id="map_union">
<code class="descname">map_union</code><span class="sig-paren">(</span><em>x(K</em>, <em>V)) -&gt; map(K</em>, <em>V</em><span class="sig-paren">)</span></dt>
<dd><p>Returns the union of all the input maps. If a key is found in multiple
input maps, that key’s value in the resulting map comes from an arbitrary input map.</p>
</dd></dl>

<dl class="function">
<dt id="multimap_agg">
<code class="descname">multimap_agg</code><span class="sig-paren">(</span><em>key</em>, <em>value) -&gt; map(K</em>, <em>array(V)</em><span class="sig-paren">)</span></dt>
<dd><p>Returns a multimap created from the input <code class="docutils literal"><span class="pre">key</span></code> / <code class="docutils literal"><span class="pre">value</span></code> pairs.
Each key can be associated with multiple values.</p>
</dd></dl>

</div>
<div class="section" id="approximate-aggregate-functions">
<h2>Approximate Aggregate Functions</h2>
<dl class="function">
<dt id="approx_distinct">
<code class="descname">approx_distinct</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the approximate number of distinct input values.
This function provides an approximation of <code class="docutils literal"><span class="pre">count(DISTINCT</span> <span class="pre">x)</span></code>.
Zero is returned if all input values are null.</p>
<p>This function should produce a standard error of 2.3%, which is the
standard deviation of the (approximately normal) error distribution over
all possible sets. It does not guarantee an upper bound on the error for
any specific input set.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">approx_distinct</code><span class="sig-paren">(</span><em>x</em>, <em>e</em><span class="sig-paren">)</span> &#x2192; bigint</dt>
<dd><p>Returns the approximate number of distinct input values.
This function provides an approximation of <code class="docutils literal"><span class="pre">count(DISTINCT</span> <span class="pre">x)</span></code>.
Zero is returned if all input values are null.</p>
<p>This function should produce a standard error of no more than <code class="docutils literal"><span class="pre">e</span></code>, which
is the standard deviation of the (approximately normal) error distribution
over all possible sets. It does not guarantee an upper bound on the error
for any specific input set. The current implementation of this function
requires that <code class="docutils literal"><span class="pre">e</span></code> be in the range of <code class="docutils literal"><span class="pre">[0.0040625,</span> <span class="pre">0.26000]</span></code>.</p>
</dd></dl>

<dl class="function">
<dt id="approx_percentile">
<code class="descname">approx_percentile</code><span class="sig-paren">(</span><em>x</em>, <em>percentage</em><span class="sig-paren">)</span> &#x2192; [same as x]</dt>
<dd><p>Returns the approximate percentile for all input values of <code class="docutils literal"><span class="pre">x</span></code> at the
given <code class="docutils literal"><span class="pre">percentage</span></code>. The value of <code class="docutils literal"><span class="pre">percentage</span></code> must be between zero and
one and must be constant for all input rows.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">approx_percentile</code><span class="sig-paren">(</span><em>x</em>, <em>percentages</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as x]&gt;</dt>
<dd><p>Returns the approximate percentile for all input values of <code class="docutils literal"><span class="pre">x</span></code> at each of
the specified percentages. Each element of the <code class="docutils literal"><span class="pre">percentages</span></code> array must be
between zero and one, and the array must be constant for all input rows.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">approx_percentile</code><span class="sig-paren">(</span><em>x</em>, <em>w</em>, <em>percentage</em><span class="sig-paren">)</span> &#x2192; [same as x]</dt>
<dd><p>Returns the approximate weighed percentile for all input values of <code class="docutils literal"><span class="pre">x</span></code>
using the per-item weight <code class="docutils literal"><span class="pre">w</span></code> at the percentage <code class="docutils literal"><span class="pre">p</span></code>. Weights must be
strictly positive. Integer-value weights can be thought of as a replication
count for the value <code class="docutils literal"><span class="pre">x</span></code> in the percentile set. The value of <code class="docutils literal"><span class="pre">p</span></code> must be
between zero and one and must be constant for all input rows.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">approx_percentile</code><span class="sig-paren">(</span><em>x</em>, <em>w</em>, <em>percentage</em>, <em>accuracy</em><span class="sig-paren">)</span> &#x2192; [same as x]</dt>
<dd><p>Returns the approximate weighed percentile for all input values of <code class="docutils literal"><span class="pre">x</span></code>
using the per-item weight <code class="docutils literal"><span class="pre">w</span></code> at the percentage <code class="docutils literal"><span class="pre">p</span></code>, with a maximum rank
error of <code class="docutils literal"><span class="pre">accuracy</span></code>. Weights must be strictly positive. Integer-value
weights can be thought of as a replication count for the value <code class="docutils literal"><span class="pre">x</span></code> in the
percentile set. The value of <code class="docutils literal"><span class="pre">p</span></code> must be between zero and one and must be
constant for all input rows. <code class="docutils literal"><span class="pre">accuracy</span></code> must be a value greater than zero
and less than one, and it must be constant for all input rows.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">approx_percentile</code><span class="sig-paren">(</span><em>x</em>, <em>w</em>, <em>percentages</em><span class="sig-paren">)</span> &#x2192; array&lt;[same as x]&gt;</dt>
<dd><p>Returns the approximate weighed percentile for all input values of <code class="docutils literal"><span class="pre">x</span></code>
using the per-item weight <code class="docutils literal"><span class="pre">w</span></code> at each of the given percentages specified
in the array. Weights must be strictly positive. Integer-value weights can
be thought of as a replication count for the value <code class="docutils literal"><span class="pre">x</span></code> in the percentile
set. Each element of the array must be between zero and one, and the array
must be constant for all input rows.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">approx_set</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; HyperLogLog</dt>
<dd><p>See <a class="reference internal" href="hyperloglog.html"><span class="doc">HyperLogLog Functions</span></a>.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">merge</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; HyperLogLog</dt>
<dd><p>See <a class="reference internal" href="hyperloglog.html"><span class="doc">HyperLogLog Functions</span></a>.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">merge</code><span class="sig-paren">(</span><em>qdigest(T)) -&gt; qdigest(T</em><span class="sig-paren">)</span></dt>
<dd><p>See <a class="reference internal" href="qdigest.html"><span class="doc">Quantile Digest Functions</span></a>.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">qdigest_agg</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; qdigest&lt;[same as x]&gt;</dt>
<dd><p>See <a class="reference internal" href="qdigest.html"><span class="doc">Quantile Digest Functions</span></a>.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">qdigest_agg</code><span class="sig-paren">(</span><em>x</em>, <em>w</em><span class="sig-paren">)</span> &#x2192; qdigest&lt;[same as x]&gt;</dt>
<dd><p>See <a class="reference internal" href="qdigest.html"><span class="doc">Quantile Digest Functions</span></a>.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">qdigest_agg</code><span class="sig-paren">(</span><em>x</em>, <em>w</em>, <em>accuracy</em><span class="sig-paren">)</span> &#x2192; qdigest&lt;[same as x]&gt;</dt>
<dd><p>See <a class="reference internal" href="qdigest.html"><span class="doc">Quantile Digest Functions</span></a>.</p>
</dd></dl>

<dl class="function">
<dt id="numeric_histogram">
<code class="descname">numeric_histogram</code><span class="sig-paren">(</span><em>buckets</em>, <em>value</em>, <em>weight</em><span class="sig-paren">)</span> &#x2192; map&lt;double, double&gt;</dt>
<dd><p>Computes an approximate histogram with up to <code class="docutils literal"><span class="pre">buckets</span></code> number of buckets
for all <code class="docutils literal"><span class="pre">value</span></code>s with a per-item weight of <code class="docutils literal"><span class="pre">weight</span></code>. The algorithm
is based loosely on:</p>
<div class="highlight-none"><div class="highlight"><pre><span></span>Yael Ben-Haim and Elad Tom-Tov, &quot;A streaming parallel decision tree algorithm&quot;,
J. Machine Learning Research 11 (2010), pp. 849--872.
</pre></div>
</div>
<p><code class="docutils literal"><span class="pre">buckets</span></code> must be a <code class="docutils literal"><span class="pre">bigint</span></code>. <code class="docutils literal"><span class="pre">value</span></code> and <code class="docutils literal"><span class="pre">weight</span></code> must be numeric.</p>
</dd></dl>

<dl class="function">
<dt>
<code class="descname">numeric_histogram</code><span class="sig-paren">(</span><em>buckets</em>, <em>value</em><span class="sig-paren">)</span> &#x2192; map&lt;double, double&gt;</dt>
<dd><p>Computes an approximate histogram with up to <code class="docutils literal"><span class="pre">buckets</span></code> number of buckets
for all <code class="docutils literal"><span class="pre">value</span></code>s. This function is equivalent to the variant of
<a class="reference internal" href="#numeric_histogram" title="numeric_histogram"><code class="xref py py-func docutils literal"><span class="pre">numeric_histogram()</span></code></a> that takes a <code class="docutils literal"><span class="pre">weight</span></code>, with a per-item weight of <code class="docutils literal"><span class="pre">1</span></code>.</p>
</dd></dl>

</div>
<div class="section" id="statistical-aggregate-functions">
<h2>Statistical Aggregate Functions</h2>
<dl class="function">
<dt id="corr">
<code class="descname">corr</code><span class="sig-paren">(</span><em>y</em>, <em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns correlation coefficient of input values.</p>
</dd></dl>

<dl class="function">
<dt id="covar_pop">
<code class="descname">covar_pop</code><span class="sig-paren">(</span><em>y</em>, <em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the population covariance of input values.</p>
</dd></dl>

<dl class="function">
<dt id="covar_samp">
<code class="descname">covar_samp</code><span class="sig-paren">(</span><em>y</em>, <em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the sample covariance of input values.</p>
</dd></dl>

<dl class="function">
<dt id="kurtosis">
<code class="descname">kurtosis</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the excess kurtosis of all input values. Unbiased estimate using
the following expression:</p>
<div class="highlight-none"><div class="highlight"><pre><span></span>kurtosis(x) = n(n+1)/((n-1)(n-2)(n-3))sum[(x_i-mean)^4]/stddev(x)^4-3(n-1)^2/((n-2)(n-3))
</pre></div>
</div>
</dd></dl>

<dl class="function">
<dt id="regr_intercept">
<code class="descname">regr_intercept</code><span class="sig-paren">(</span><em>y</em>, <em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns linear regression intercept of input values. <code class="docutils literal"><span class="pre">y</span></code> is the dependent
value. <code class="docutils literal"><span class="pre">x</span></code> is the independent value.</p>
</dd></dl>

<dl class="function">
<dt id="regr_slope">
<code class="descname">regr_slope</code><span class="sig-paren">(</span><em>y</em>, <em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns linear regression slope of input values. <code class="docutils literal"><span class="pre">y</span></code> is the dependent
value. <code class="docutils literal"><span class="pre">x</span></code> is the independent value.</p>
</dd></dl>

<dl class="function">
<dt id="skewness">
<code class="descname">skewness</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the skewness of all input values.</p>
</dd></dl>

<dl class="function">
<dt id="stddev">
<code class="descname">stddev</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>This is an alias for <a class="reference internal" href="#stddev_samp" title="stddev_samp"><code class="xref py py-func docutils literal"><span class="pre">stddev_samp()</span></code></a>.</p>
</dd></dl>

<dl class="function">
<dt id="stddev_pop">
<code class="descname">stddev_pop</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the population standard deviation of all input values.</p>
</dd></dl>

<dl class="function">
<dt id="stddev_samp">
<code class="descname">stddev_samp</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the sample standard deviation of all input values.</p>
</dd></dl>

<dl class="function">
<dt id="variance">
<code class="descname">variance</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>This is an alias for <a class="reference internal" href="#var_samp" title="var_samp"><code class="xref py py-func docutils literal"><span class="pre">var_samp()</span></code></a>.</p>
</dd></dl>

<dl class="function">
<dt id="var_pop">
<code class="descname">var_pop</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the population variance of all input values.</p>
</dd></dl>

<dl class="function">
<dt id="var_samp">
<code class="descname">var_samp</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span> &#x2192; double</dt>
<dd><p>Returns the sample variance of all input values.</p>
</dd></dl>

</div>
<div class="section" id="lambda-aggregate-functions">
<h2>Lambda Aggregate Functions</h2>
<dl class="function">
<dt id="reduce_agg">
<code class="descname">reduce_agg</code><span class="sig-paren">(</span><em>inputValue T</em>, <em>initialState S</em>, <em>inputFunction(S</em>, <em>T</em>, <em>S)</em>, <em>combineFunction(S</em>, <em>S</em>, <em>S)</em><span class="sig-paren">)</span> &#x2192; S</dt>
<dd><p>Reduces all input values into a single value. <code class="docutils literal"><span class="pre">inputFunction</span></code> will be invoked
for each non-null input value. In addition to taking the input value, <code class="docutils literal"><span class="pre">inputFunction</span></code>
takes the current state, initially <code class="docutils literal"><span class="pre">initialState</span></code>, and returns the new state.
<code class="docutils literal"><span class="pre">combineFunction</span></code> will be invoked to combine two states into a new state.
The final state is returned:</p>
<div class="highlight-sql"><div class="highlight"><pre><span></span><span class="k">SELECT</span> <span class="n">id</span><span class="p">,</span> <span class="n">reduce_agg</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span><span class="p">)</span>
<span class="k">FROM</span> <span class="p">(</span>
    <span class="k">VALUES</span>
        <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
<span class="p">)</span> <span class="k">AS</span> <span class="n">t</span><span class="p">(</span><span class="n">id</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
<span class="k">GROUP</span> <span class="k">BY</span> <span class="n">id</span><span class="p">;</span>
<span class="c1">-- (1, 12)</span>
<span class="c1">-- (2, 13)</span>

<span class="k">SELECT</span> <span class="n">id</span><span class="p">,</span> <span class="n">reduce_agg</span><span class="p">(</span><span class="n">value</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">a</span> <span class="o">*</span> <span class="n">b</span><span class="p">)</span>
<span class="k">FROM</span> <span class="p">(</span>
    <span class="k">VALUES</span>
        <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">5</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">),</span>
        <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">7</span><span class="p">)</span>
<span class="p">)</span> <span class="k">AS</span> <span class="n">t</span><span class="p">(</span><span class="n">id</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
<span class="k">GROUP</span> <span class="k">BY</span> <span class="n">id</span><span class="p">;</span>
<span class="c1">-- (1, 60)</span>
<span class="c1">-- (2, 42)</span>
</pre></div>
</div>
<p>The state type must be a boolean, integer, floating-point, or date/time/interval.</p>
</dd></dl>

</div>
</div>


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