assertEquals( 0.691462, GaussianDistribution::cumulativeTo(0.5),'', GaussianDistributionTest::ERROR_TOLERANCE); } public function testAt() { // Verified with WolframAlpha // (e.g. http://www.wolframalpha.com/input/?i=PDF%5BNormalDistribution%5B0%2C1%5D%2C+0.5%5D ) $this->assertEquals(0.352065, GaussianDistribution::at(0.5), '', GaussianDistributionTest::ERROR_TOLERANCE); } public function testMultiplication() { // I verified this against the formula at http://www.tina-vision.net/tina-knoppix/tina-memo/2003-003.pdf $standardNormal = new GaussianDistribution(0, 1); $shiftedGaussian = new GaussianDistribution(2, 3); $product = GaussianDistribution::multiply($standardNormal, $shiftedGaussian); $this->assertEquals(0.2, $product->getMean(), '', GaussianDistributionTest::ERROR_TOLERANCE); $this->assertEquals(3.0 / sqrt(10), $product->getStandardDeviation(), '', GaussianDistributionTest::ERROR_TOLERANCE); $m4s5 = new GaussianDistribution(4, 5); $m6s7 = new GaussianDistribution(6, 7); $product2 = GaussianDistribution::multiply($m4s5, $m6s7); $expectedMean = (4 * square(7) + 6 * square(5)) / (square(5) + square(7)); $this->assertEquals($expectedMean, $product2->getMean(), '', GaussianDistributionTest::ERROR_TOLERANCE); $expectedSigma = sqrt(((square(5) * square(7)) / (square(5) + square(7)))); $this->assertEquals($expectedSigma, $product2->getStandardDeviation(), '', GaussianDistributionTest::ERROR_TOLERANCE); } public function testDivision() { // Since the multiplication was worked out by hand, we use the same numbers but work backwards $product = new GaussianDistribution(0.2, 3.0 / sqrt(10)); $standardNormal = new GaussianDistribution(0, 1); $productDividedByStandardNormal = GaussianDistribution::divide($product, $standardNormal); $this->assertEquals(2.0, $productDividedByStandardNormal->getMean(), '', GaussianDistributionTest::ERROR_TOLERANCE); $this->assertEquals(3.0, $productDividedByStandardNormal->getStandardDeviation(),'', GaussianDistributionTest::ERROR_TOLERANCE); $product2 = new GaussianDistribution((4 * square(7) + 6 * square(5)) / (square(5) + square(7)), sqrt(((square(5) * square(7)) / (square(5) + square(7))))); $m4s5 = new GaussianDistribution(4,5); $product2DividedByM4S5 = GaussianDistribution::divide($product2, $m4s5); $this->assertEquals(6.0, $product2DividedByM4S5->getMean(), '', GaussianDistributionTest::ERROR_TOLERANCE); $this->assertEquals(7.0, $product2DividedByM4S5->getStandardDeviation(), '', GaussianDistributionTest::ERROR_TOLERANCE); } public function testLogProductNormalization() { // Verified with Ralf Herbrich's F# implementation $standardNormal = new GaussianDistribution(0, 1); $lpn = GaussianDistribution::logProductNormalization($standardNormal, $standardNormal); $this->assertEquals(-1.2655121234846454, $lpn, '', GaussianDistributionTest::ERROR_TOLERANCE); $m1s2 = new GaussianDistribution(1, 2); $m3s4 = new GaussianDistribution(3, 4); $lpn2 = GaussianDistribution::logProductNormalization($m1s2, $m3s4); $this->assertEquals(-2.5168046699816684, $lpn2, '', GaussianDistributionTest::ERROR_TOLERANCE); } public function testLogRatioNormalization() { // Verified with Ralf Herbrich's F# implementation $m1s2 = new GaussianDistribution(1, 2); $m3s4 = new GaussianDistribution(3, 4); $lrn = GaussianDistribution::logRatioNormalization($m1s2, $m3s4); $this->assertEquals(2.6157405972171204, $lrn, '', GaussianDistributionTest::ERROR_TOLERANCE); } public function testAbsoluteDifference() { // Verified with Ralf Herbrich's F# implementation $standardNormal = new GaussianDistribution(0, 1); $absDiff = GaussianDistribution::absoluteDifference($standardNormal, $standardNormal); $this->assertEquals(0.0, $absDiff, '', GaussianDistributionTest::ERROR_TOLERANCE); $m1s2 = new GaussianDistribution(1, 2); $m3s4 = new GaussianDistribution(3, 4); $absDiff2 = GaussianDistribution::absoluteDifference($m1s2, $m3s4); $this->assertEquals(0.4330127018922193, $absDiff2, '', GaussianDistributionTest::ERROR_TOLERANCE); } } ?>