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fix: return the limiting density at x = 0 in stats/base/dists/betaprime/logpdf and pdf #15607

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fix: return the limiting density at x = 0 in stats/base/dists/betaprime/logpdf and pdf #15607

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15 changes: 13 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/factory.js
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Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,7 @@ var betaln = require( '@stdlib/math/base/special/betaln' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var ln = require( '@stdlib/math/base/special/ln' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );


Expand Down Expand Up @@ -75,10 +76,20 @@ function factory( alpha, beta ) {
if ( isnan( x ) ) {
return NaN;
}
if ( x <= 0.0 ) {
// Support of the beta prime distribution: (0,∞)
if ( x < 0.0 ) {
// Support of the beta prime distribution: [0,∞)
return NINF;
}
// At `x = 0`, the density is infinite for `alpha < 1`, `1/B(1,beta) = beta` for `alpha = 1`, and `0` for `alpha > 1`:
if ( x === 0.0 ) {
if ( alpha < 1.0 ) {
return PINF;
}
if ( alpha > 1.0 ) {
return NINF;
}
return ln( beta );
}
out = ( alpha-1.0 ) * ln( x );
out -= ( alpha+beta ) * log1p( x );
out -= betalnAB;
Expand Down
15 changes: 13 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/main.js
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Expand Up @@ -24,6 +24,7 @@ var betaln = require( '@stdlib/math/base/special/betaln' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var log1p = require( '@stdlib/math/base/special/log1p' );
var ln = require( '@stdlib/math/base/special/ln' );
var PINF = require( '@stdlib/constants/float64/pinf' );
var NINF = require( '@stdlib/constants/float64/ninf' );


Expand Down Expand Up @@ -89,10 +90,20 @@ function logpdf( x, alpha, beta ) {
) {
return NaN;
}
if ( x <= 0.0 ) {
// Support of the beta prime distribution: (0,∞)
if ( x < 0.0 ) {
// Support of the beta prime distribution: [0,∞)
return NINF;
}
// At `x = 0`, the density is infinite for `alpha < 1`, `1/B(1,beta) = beta` for `alpha = 1`, and `0` for `alpha > 1`:
if ( x === 0.0 ) {
if ( alpha < 1.0 ) {
return PINF;
}
if ( alpha > 1.0 ) {
return NINF;
}
return ln( beta );
}
out = ( alpha-1.0 ) * ln( x );
out -= ( alpha+beta ) * log1p( x );
out -= betaln( alpha, beta );
Expand Down
3 changes: 3 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/manifest.json
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Expand Up @@ -43,6 +43,7 @@
"@stdlib/math/base/special/betaln",
"@stdlib/math/base/special/log1p",
"@stdlib/math/base/special/ln",
"@stdlib/constants/float64/pinf",
"@stdlib/constants/float64/ninf"
]
},
Expand All @@ -62,6 +63,7 @@
"@stdlib/math/base/special/betaln",
"@stdlib/math/base/special/log1p",
"@stdlib/math/base/special/ln",
"@stdlib/constants/float64/pinf",
"@stdlib/constants/float64/ninf",
"@stdlib/constants/float64/eps"
]
Expand All @@ -82,6 +84,7 @@
"@stdlib/math/base/special/betaln",
"@stdlib/math/base/special/log1p",
"@stdlib/math/base/special/ln",
"@stdlib/constants/float64/pinf",
"@stdlib/constants/float64/ninf",
"@stdlib/constants/float64/eps"
]
Expand Down
15 changes: 13 additions & 2 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/src/main.c
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Expand Up @@ -20,6 +20,7 @@
#include "stdlib/math/base/special/betaln.h"
#include "stdlib/math/base/special/log1p.h"
#include "stdlib/math/base/special/ln.h"
#include "stdlib/constants/float64/pinf.h"
#include "stdlib/constants/float64/ninf.h"

/**
Expand All @@ -45,10 +46,20 @@ double stdlib_base_dists_betaprime_logpdf( const double x, const double alpha, c
) {
return 0.0 / 0.0;
}
if ( x <= 0.0 ) {
// Support of the beta prime distribution: (0,∞)
if ( x < 0.0 ) {
// Support of the beta prime distribution: [0,∞)
return STDLIB_CONSTANT_FLOAT64_NINF;
}
// At `x = 0`, the density is infinite for `alpha < 1`, `1/B(1,beta) = beta` for `alpha = 1`, and `0` for `alpha > 1`:
if ( x == 0.0 ) {
if ( alpha < 1.0 ) {
return STDLIB_CONSTANT_FLOAT64_PINF;
}
if ( alpha > 1.0 ) {
return STDLIB_CONSTANT_FLOAT64_NINF;
}
return stdlib_base_ln( beta );
}
out = ( alpha-1.0 ) * stdlib_base_ln( x );
out -= ( alpha+beta ) * stdlib_base_log1p( x );
out -= stdlib_base_betaln( alpha, beta );
Expand Down
16 changes: 16 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.factory.js
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Expand Up @@ -21,6 +21,7 @@
// MODULES //

var tape = require( 'tape' );
var ln = require( '@stdlib/math/base/special/ln' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
var PINF = require( '@stdlib/constants/float64/pinf' );
Expand Down Expand Up @@ -94,6 +95,21 @@ tape( 'if provided a valid `alpha` and `beta`, the function returns a function w
t.end();
});

tape( 'the created function returns `+infinity`, `ln(beta)`, or `-infinity` at `x = 0` when `alpha` is less than, equal to, or greater than one', function test( t ) {
var logpdf;

logpdf = factory( 0.5, 2.0 );
t.strictEqual( logpdf( 0.0 ), PINF, 'returns expected value' );

logpdf = factory( 1.0, 2.0 );
t.strictEqual( logpdf( 0.0 ), ln( 2.0 ), 'returns expected value' );

logpdf = factory( 3.0, 2.0 );
t.strictEqual( logpdf( 0.0 ), NINF, 'returns expected value' );

t.end();
});

tape( 'if provided `beta <= 0`, the created function always returns `NaN`', function test( t ) {
var logpdf;
var y;
Expand Down
8 changes: 8 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.logpdf.js
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Expand Up @@ -21,6 +21,7 @@
// MODULES //

var tape = require( 'tape' );
var ln = require( '@stdlib/math/base/special/ln' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var abs = require( '@stdlib/math/base/special/abs' );
var PINF = require( '@stdlib/constants/float64/pinf' );
Expand Down Expand Up @@ -69,6 +70,13 @@ tape( 'if provided a number smaller than zero for `x` and a valid `alpha` and `b
t.end();
});

tape( 'the function returns `+infinity`, `ln(beta)`, or `-infinity` at `x = 0` when `alpha` is less than, equal to, or greater than one', function test( t ) {
t.strictEqual( logpdf( 0.0, 0.5, 2.0 ), PINF, 'returns expected value' );
t.strictEqual( logpdf( 0.0, 1.0, 2.0 ), ln( 2.0 ), 'returns expected value' );
t.strictEqual( logpdf( 0.0, 3.0, 2.0 ), NINF, 'returns expected value' );
t.end();
});

tape( 'if provided `alpha <= 0`, the function returns `NaN`', function test( t ) {
var y;

Expand Down
8 changes: 8 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.native.js
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Expand Up @@ -22,6 +22,7 @@

var resolve = require( 'path' ).resolve;
var tape = require( 'tape' );
var ln = require( '@stdlib/math/base/special/ln' );
var isnan = require( '@stdlib/math/base/assert/is-nan' );
var tryRequire = require( '@stdlib/utils/try-require' );
var abs = require( '@stdlib/math/base/special/abs' );
Expand Down Expand Up @@ -78,6 +79,13 @@ tape( 'if provided a number smaller than zero for `x` and a valid `alpha` and `b
t.end();
});

tape( 'the function returns `+infinity`, `ln(beta)`, or `-infinity` at `x = 0` when `alpha` is less than, equal to, or greater than one', opts, function test( t ) {
t.strictEqual( logpdf( 0.0, 0.5, 2.0 ), PINF, 'returns expected value' );
t.strictEqual( logpdf( 0.0, 1.0, 2.0 ), ln( 2.0 ), 'returns expected value' );
t.strictEqual( logpdf( 0.0, 3.0, 2.0 ), NINF, 'returns expected value' );
t.end();
});

tape( 'if provided `alpha <= 0`, the function returns `NaN`', opts, function test( t ) {
var y;

Expand Down
18 changes: 15 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.factory.js
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Expand Up @@ -76,7 +76,7 @@ tape( 'if provided `NaN` for any parameter, the created function returns `NaN`',
t.end();
});

tape( 'if provided a valid `alpha` and `beta`, the function returns a function which returns `0` when provided a nonpositive number for `x`', function test( t ) {
tape( 'if provided a valid `alpha` and `beta`, the function returns a function which returns `0` when provided a negative number for `x`', function test( t ) {
var pdf;
var y;

Expand All @@ -90,8 +90,20 @@ tape( 'if provided a valid `alpha` and `beta`, the function returns a function w
y = pdf( -0.5 );
t.strictEqual( y, 0.0, 'returns expected value' );

y = pdf( 0.0 );
t.strictEqual( y, 0.0, 'returns expected value' );
t.end();
});

tape( 'the created function returns `+infinity`, `beta`, or `0` at `x = 0` when `alpha` is less than, equal to, or greater than one', function test( t ) {
var pdf;

pdf = factory( 0.5, 2.0 );
t.strictEqual( pdf( 0.0 ), PINF, 'returns expected value' );

pdf = factory( 1.0, 2.0 );
t.strictEqual( pdf( 0.0 ), 2.0, 'returns expected value' );

pdf = factory( 3.0, 2.0 );
t.strictEqual( pdf( 0.0 ), 0.0, 'returns expected value' );

t.end();
});
Expand Down
10 changes: 7 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.native.js
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Expand Up @@ -62,7 +62,7 @@ tape( 'if provided `NaN` for any parameter, the function returns `NaN`', opts, f
t.end();
});

tape( 'if provided a nonpositive number for `x` and a valid `alpha` and `beta`, the function returns `0`', opts, function test( t ) {
tape( 'if provided a negative number for `x` and a valid `alpha` and `beta`, the function returns `0`', opts, function test( t ) {
var y;

y = pdf( NINF, 1.0, 1.0 );
Expand All @@ -74,9 +74,13 @@ tape( 'if provided a nonpositive number for `x` and a valid `alpha` and `beta`,
y = pdf( -0.5, 1.0, 1.0 );
t.strictEqual( y, 0.0, 'returns expected value' );

y = pdf( 0.0, 1.0, 1.0 );
t.strictEqual( y, 0.0, 'returns expected value' );
t.end();
});

tape( 'the function returns `+infinity`, `beta`, or `0` at `x = 0` when `alpha` is less than, equal to, or greater than one', opts, function test( t ) {
t.strictEqual( pdf( 0.0, 0.5, 2.0 ), PINF, 'returns expected value' );
t.strictEqual( pdf( 0.0, 1.0, 2.0 ), 2.0, 'returns expected value' );
t.strictEqual( pdf( 0.0, 3.0, 2.0 ), 0.0, 'returns expected value' );
t.end();
});

Expand Down
10 changes: 7 additions & 3 deletions lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.pdf.js
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Expand Up @@ -53,7 +53,7 @@ tape( 'if provided `NaN` for any parameter, the function returns `NaN`', functio
t.end();
});

tape( 'if provided a nonpositive number for `x` and a valid `alpha` and `beta`, the function returns `0`', function test( t ) {
tape( 'if provided a negative number for `x` and a valid `alpha` and `beta`, the function returns `0`', function test( t ) {
var y;

y = pdf( NINF, 1.0, 1.0 );
Expand All @@ -65,9 +65,13 @@ tape( 'if provided a nonpositive number for `x` and a valid `alpha` and `beta`,
y = pdf( -0.5, 1.0, 1.0 );
t.strictEqual( y, 0.0, 'returns expected value' );

y = pdf( 0.0, 1.0, 1.0 );
t.strictEqual( y, 0.0, 'returns expected value' );
t.end();
});

tape( 'the function returns `+infinity`, `beta`, or `0` at `x = 0` when `alpha` is less than, equal to, or greater than one', function test( t ) {
t.strictEqual( pdf( 0.0, 0.5, 2.0 ), PINF, 'returns expected value' );
t.strictEqual( pdf( 0.0, 1.0, 2.0 ), 2.0, 'returns expected value' );
t.strictEqual( pdf( 0.0, 3.0, 2.0 ), 0.0, 'returns expected value' );
t.end();
});

Expand Down
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