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Task/Benfords-law/PL-pgSQL/benfords-law.sql

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+WITH recursive
+constant(val) AS
+(
+select 1000.
+)
+,
+fib(a,b) AS
+(
+SELECT CAST(0 AS numeric), CAST(1 AS numeric)
+UNION ALL
+SELECT b,a+b
+FROM fib
+)
+,
+benford(first_digit, probability_real, probability_theoretical) AS
+(
+SELECT *,
+	CAST(log(1. + 1./CAST(first_digit AS INT)) AS NUMERIC(5,4)) probability_theoretical
+FROM (
+	SELECT  first_digit, CAST(COUNT(1)/(select val from constant) AS NUMERIC(5,4)) probability_real FROM
+	(
+		SELECT SUBSTRING(CAST(a AS VARCHAR(100)),1,1) first_digit
+		FROM fib
+		WHERE SUBSTRING(CAST(a AS VARCHAR(100)),1,1) <> '0'
+		LIMIT (select val from constant)
+	) t
+	GROUP BY first_digit
+) f
+ORDER BY first_digit ASC
+)
+select *
+from benford cross join
+     (select cast(corr(probability_theoretical,probability_real) as numeric(5,4)) correlation
+      from benford) c