diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/factory.js index 2e3e90550340..11ab9db41bf3 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/factory.js @@ -77,9 +77,9 @@ function factory( d1, d2 ) { return 1.0; } if ( d1 * x > d2 ) { - return betainc( (d1*x)/(d2+(d1*x)), d1/2.0, d2/2.0, true, false ); + return betainc( d2/(d2+(d1*x)), d2/2.0, d1/2.0, true, true ); } - return betainc( d2/(d2+(d1*x)), d2/2.0, d1/2.0, true, true ); + return betainc( (d1*x)/(d2+(d1*x)), d1/2.0, d2/2.0, true, false ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/main.js index bd679dc20d5a..c256df515b3a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/main.js @@ -30,6 +30,16 @@ var PINF = require( '@stdlib/constants/float64/pinf' ); /** * Evaluates the cumulative distribution function (CDF) for an F distribution with numerator degrees of freedom `d1` and denominator degrees of freedom `d2` at a value `x`. * +* ## Method +* +* The CDF is the regularized incomplete beta function evaluated at \\(z = d_1 x / (d_2 + d_1 x)\\): +* +* ```tex +* F(x;d_1,d_2) = I_{z}\left(\tfrac{d_1}{2}, \tfrac{d_2}{2}\right) = 1 - I_{1-z}\left(\tfrac{d_2}{2}, \tfrac{d_1}{2}\right) +* ``` +* +* To avoid rounding an argument close to one, the function passes \\(z\\) to the lower tail when \\(z \leq 1/2\\) (i.e., \\(d_1 x \leq d_2\\)), and \\(1-z = d_2/(d_2 + d_1 x)\\) to the upper tail otherwise. +* * @param {number} x - input value * @param {PositiveNumber} d1 - numerator degrees of freedom * @param {PositiveNumber} d2 - denominator degrees of freedom @@ -92,9 +102,9 @@ function cdf( x, d1, d2 ) { return 1.0; } if ( d1 * x > d2 ) { - return betainc( (d1*x)/(d2+(d1*x)), d1/2.0, d2 /2.0, true, false ); + return betainc( d2/(d2+(d1*x)), d2/2.0, d1/2.0, true, true ); } - return betainc( d2/(d2+(d1*x)), d2/2.0, d1/2.0, true, true ); + return betainc( (d1*x)/(d2+(d1*x)), d1/2.0, d2/2.0, true, false ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/runner.jl index 6b0bee3d1494..c8726a5c9d08 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/runner.jl @@ -87,3 +87,8 @@ x = rand( 1000 ) .* 20.0; d2 = ( rand( 1000 ) .* 20.0 ) .+ 10.0; d2 = ( rand( 1000 ) .* 20.0 ) .+ 10.0; gen( x, d1, d2, "both_large.json" ); + +x = exp10.( rand( 1000 ) .* -20.0 ); +d1 = ( rand( 1000 ) .* 20.0 ) .+ 0.5; +d2 = ( rand( 1000 ) .* 20.0 ) .+ 0.5; +gen( x, d1, d2, "small_x.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/small_x.json b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/small_x.json new file mode 100644 index 000000000000..3918b3a0ac09 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/small_x.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.cdf.js b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.cdf.js index 0359ccf1b98f..73dc751e024a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.cdf.js +++ b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.cdf.js @@ -33,6 +33,7 @@ var cdf = require( './../lib' ); var largeD1 = require( './fixtures/julia/large_d1.json' ); var largeD2 = require( './fixtures/julia/large_d2.json' ); var bothLarge = require( './fixtures/julia/both_large.json' ); +var smallX = require( './fixtures/julia/small_x.json' ); // TESTS // @@ -127,7 +128,7 @@ tape( 'the function evaluates the cdf for `x` given large `d1` and `d2`', functi d2 = bothLarge.d2; for ( i = 0; i < x.length; i++ ) { y = cdf( x[i], d1[i], d2[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 58 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 10 ), true, 'returns expected value' ); } t.end(); }); @@ -146,7 +147,7 @@ tape( 'the function evaluates the cdf for `x` given large parameter `d1`', funct d2 = largeD1.d2; for ( i = 0; i < x.length; i++ ) { y = cdf( x[i], d1[i], d2[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 542 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 17 ), true, 'returns expected value' ); } t.end(); }); @@ -165,7 +166,26 @@ tape( 'the function evaluates the cdf for `x` given large scale parameter `d2`', d2 = largeD2.d2; for ( i = 0; i < x.length; i++ ) { y = cdf( x[i], d1[i], d2[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 171 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 16 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function evaluates the cdf for small `x`', function test( t ) { + var expected; + var d1; + var d2; + var x; + var y; + var i; + + expected = smallX.expected; + x = smallX.x; + d1 = smallX.d1; + d2 = smallX.d2; + for ( i = 0; i < x.length; i++ ) { + y = cdf( x[i], d1[i], d2[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 520 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.factory.js index 0514ab5e9da4..123858673ff2 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.factory.js +++ b/lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.factory.js @@ -33,6 +33,7 @@ var factory = require( './../lib/factory.js' ); var largeD1 = require( './fixtures/julia/large_d1.json' ); var largeD2 = require( './fixtures/julia/large_d2.json' ); var bothLarge = require( './fixtures/julia/both_large.json' ); +var smallX = require( './fixtures/julia/small_x.json' ); // TESTS // @@ -178,7 +179,7 @@ tape( 'the created function evaluates the cdf for `x` given large `d1` and `d2`' for ( i = 0; i < x.length; i++ ) { cdf = factory( d1[i], d2[i] ); y = cdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 58 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 10 ), true, 'returns expected value' ); } t.end(); }); @@ -199,7 +200,7 @@ tape( 'the created function evaluates the cdf for `x` given large parameter `d1` for ( i = 0; i < x.length; i++ ) { cdf = factory( d1[i], d2[i] ); y = cdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 542 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 17 ), true, 'returns expected value' ); } t.end(); }); @@ -220,7 +221,28 @@ tape( 'the created function evaluates the cdf for `x` given large parameter `d2` for ( i = 0; i < x.length; i++ ) { cdf = factory( d1[i], d2[i] ); y = cdf( x[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 171 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 16 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the created function evaluates the cdf for small `x`', function test( t ) { + var expected; + var cdf; + var d1; + var d2; + var i; + var x; + var y; + + expected = smallX.expected; + x = smallX.x; + d1 = smallX.d1; + d2 = smallX.d2; + for ( i = 0; i < x.length; i++ ) { + cdf = factory( d1[i], d2[i] ); + y = cdf( x[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 520 ), true, 'returns expected value' ); } t.end(); });