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Add beta_cdf and inverse_beta_cdf math functions. #11981

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Add beta_cdf and inverse_beta_cdf math functions. #11981

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2046232
Add beta_cdf and inverse_beta_cdf math functions.
Nov 26, 2018
e9008f1
Fix indentation and docs wording
Nov 26, 2018
d546392
Address comments. Change to cheaper constructor and formatting.
Nov 28, 2018
cc00e93
Improve error messages.
Nov 30, 2018
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12 changes: 12 additions & 0 deletions presto-docs/src/main/sphinx/functions/math.rst
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Expand Up @@ -73,6 +73,18 @@ Mathematical Functions
The mean and value v must be real values and the standard deviation must be a real
and positive value.

.. function:: inverse_beta_cdf(a, b, p) -> double

Compute the inverse of the Beta cdf with given a, b parameters for the cumulative
probability (p): P(N < n). The a, b parameters must be positive real values.
The probability p must lie on the interval [0, 1].

.. function:: beta_cdf(a, b, v) -> double

Compute the Beta cdf with given a, b parameters: P(N < v; a, b).
The a, b parameters must be positive real numbers and value v must be a real value.
The value v must lie on the interval [0, 1].

.. function:: ln(x) -> double

Returns the natural logarithm of ``x``.
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31 changes: 31 additions & 0 deletions presto-main/src/main/java/com/facebook/presto/operator/scalar/MathFunctions.java
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Expand Up @@ -30,6 +30,7 @@
import com.facebook.presto.type.LiteralParameter;
import com.google.common.primitives.Doubles;
import io.airlift.slice.Slice;
import org.apache.commons.math3.distribution.BetaDistribution;
import org.apache.commons.math3.special.Erf;

import java.math.BigInteger;
Expand Down Expand Up @@ -629,6 +630,36 @@ public static double normalCdf(
return 0.5 * (1 + Erf.erf((value - mean) / (standardDeviation * Math.sqrt(2))));
}

@Description("inverse of Beta cdf given a, b parameters and probability")
@ScalarFunction
@SqlType(StandardTypes.DOUBLE)
public static double inverseBetaCdf(
@SqlType(StandardTypes.DOUBLE) double a,
@SqlType(StandardTypes.DOUBLE) double b,
@SqlType(StandardTypes.DOUBLE) double p)
{
checkCondition(p >= 0 && p <= 1, INVALID_FUNCTION_ARGUMENT, "p must be in the interval [0, 1]");
checkCondition(a > 0, INVALID_FUNCTION_ARGUMENT, "a must be > 0");
checkCondition(b > 0, INVALID_FUNCTION_ARGUMENT, "b must be > 0");
BetaDistribution distribution = new BetaDistribution(null, a, b, BetaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
return distribution.inverseCumulativeProbability(p);
}

@Description("Beta cdf given the a, b parameters and value")
@ScalarFunction
@SqlType(StandardTypes.DOUBLE)
public static double betaCdf(
@SqlType(StandardTypes.DOUBLE) double a,
@SqlType(StandardTypes.DOUBLE) double b,
@SqlType(StandardTypes.DOUBLE) double value)
{
checkCondition(value >= 0 && value <= 1, INVALID_FUNCTION_ARGUMENT, "value must be in the interval [0, 1]");
checkCondition(a > 0, INVALID_FUNCTION_ARGUMENT, "a must be > 0");
checkCondition(b > 0, INVALID_FUNCTION_ARGUMENT, "b must be > 0");
BetaDistribution distribution = new BetaDistribution(null, a, b, BetaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
return distribution.cumulativeProbability(value);
}

@Description("round to nearest integer")
@ScalarFunction("round")
@SqlType(StandardTypes.TINYINT)
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29 changes: 29 additions & 0 deletions presto-main/src/test/java/com/facebook/presto/operator/scalar/TestMathFunctions.java
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Expand Up @@ -1343,6 +1343,35 @@ public void testNormalCdf()
assertInvalidFunction("normal_cdf(0, nan(), 0.1985)", "standardDeviation must > 0");
}

@Test
public void testInverseBetaCdf()
{
assertFunction("inverse_beta_cdf(3, 3.6, 0.0)", DOUBLE, 0.0);
assertFunction("inverse_beta_cdf(3, 3.6, 1.0)", DOUBLE, 1.0);
assertFunction("inverse_beta_cdf(3, 3.6, 0.3)", DOUBLE, 0.3469675485440618);
assertFunction("inverse_beta_cdf(3, 3.6, 0.95)", DOUBLE, 0.7600272463100223);

assertInvalidFunction("inverse_beta_cdf(0, 3, 0.5)", "a must be > 0");
assertInvalidFunction("inverse_beta_cdf(3, 0, 0.5)", "b must be > 0");
assertInvalidFunction("inverse_beta_cdf(3, 5, -0.1)", "p must be in the interval [0, 1]");
assertInvalidFunction("inverse_beta_cdf(3, 5, 1.1)", "p must be in the interval [0, 1]");
}

@Test
public void testBetaCdf()
throws Exception
{
assertFunction("beta_cdf(3, 3.6, 0.0)", DOUBLE, 0.0);
assertFunction("beta_cdf(3, 3.6, 1.0)", DOUBLE, 1.0);
assertFunction("beta_cdf(3, 3.6, 0.3)", DOUBLE, 0.21764809997679938);
assertFunction("beta_cdf(3, 3.6, 0.9)", DOUBLE, 0.9972502881611551);

assertInvalidFunction("beta_cdf(0, 3, 0.5)", "a must be > 0");
assertInvalidFunction("beta_cdf(3, 0, 0.5)", "b must be > 0");
assertInvalidFunction("beta_cdf(3, 5, -0.1)", "value must be in the interval [0, 1]");
assertInvalidFunction("beta_cdf(3, 5, 1.1)", "value must be in the interval [0, 1]");
}

@Test
public void testWilsonInterval()
{
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