Merge pull request #124 from CartoDB/add-kurtosis

Add kurtosis and skewness

scripts-available/CDB_Stats.sql

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+--
+-- Calculate basic statistics of a given dataset
+--
+-- @param in_array A numeric array of numbers
+--
+-- Returns: statistical quantity chosen
+-- 
+-- References: http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
+--
+
+-- Calculate kurtosis
+CREATE OR REPLACE FUNCTION CDB_Kurtosis ( in_array NUMERIC[] ) RETURNS NUMERIC as $$
+DECLARE
+    a numeric;
+    c numeric;
+    s numeric;
+    k numeric;
+BEGIN
+    SELECT AVG(e), COUNT(e)::numeric, stddev(e) INTO a, c, s FROM ( SELECT unnest(in_array) e ) x;
+
+    EXECUTE 'SELECT sum(power($1 - e, 4)) / ( $2 * power($3, 4)) - 3
+             FROM (SELECT unnest($4) e ) x'
+    INTO k
+    USING a, c, s, in_array;
+
+    RETURN k;
+END;
+$$ language plpgsql IMMUTABLE;
+
+-- Calculate skewness
+CREATE OR REPLACE FUNCTION CDB_Skewness ( in_array NUMERIC[] ) RETURNS NUMERIC as $$
+DECLARE
+    a numeric;
+    c numeric;
+    s numeric;
+    sk numeric;
+BEGIN
+    SELECT AVG(e), COUNT(e)::numeric, stddev(e) INTO a, c, s FROM ( SELECT unnest(in_array) e ) x;
+
+    EXECUTE 'SELECT sum(power($1 - e, 3)) / ( $2 * power($3, 3))
+             FROM (SELECT unnest($4) e ) x'
+    INTO sk
+    USING a, c, s, in_array;
+
+    RETURN sk;
+END;
+$$ language plpgsql IMMUTABLE;

scripts-enabled/CDB_Stats.sql

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+../scripts-available/CDB_Stats.sql

test/CDB_StatsTest.sql

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+-- continuous uniform distribution has kurtosis = -6/5, skewness = 0.0
+-- http://mathworld.wolfram.com/UniformDistribution.html
+set client_min_messages to ERROR;
+
+With dist As (
+  SELECT random()::numeric As val
+  FROM generate_series(1,50000) t
+)
+
+SELECT 
+  -- does random dist values match within 1% of known values
+  abs(CDB_Kurtosis(array_agg(val)) + 1.20) < 1e-2 As kurtosis,
+  abs(CDB_Skewness(array_agg(val)) - 0) < 1e-2 As skewness
+FROM dist;
+
+set client_min_messages to NOTICE;

test/CDB_StatsTest_expect

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+SET
+t|t
+SET