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fix: pass betainc the argument below one half in stats/base/dists/f/cdf #15603

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fix: pass betainc the argument below one half in stats/base/dists/f/cdf #15603

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35b0dbe
fix: pass `betainc` the argument below one half in `stats/base/dists/…
Abhist17 Sep 27, 2026
07aac1e
docs: document the method in the JSDoc
Abhist17 Sep 28, 2026
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4 changes: 2 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/factory.js
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Original file line number Diff line number Diff line change
Expand Up @@ -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 );
}
}

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14 changes: 12 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dists/f/cdf/lib/main.js
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Expand Up @@ -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
Expand Down Expand Up @@ -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 );
}


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5 changes: 5 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/runner.jl
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Expand Up @@ -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" );
1 change: 1 addition & 0 deletions lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/fixtures/julia/small_x.json
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26 changes: 23 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.cdf.js
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Expand Up @@ -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 //
Expand Down Expand Up @@ -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();
});
Expand All @@ -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();
});
Expand All @@ -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();
});
28 changes: 25 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/f/cdf/test/test.factory.js
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Original file line number Diff line number Diff line change
Expand Up @@ -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 //
Expand Down Expand Up @@ -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();
});
Expand All @@ -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();
});
Expand All @@ -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();
});
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