diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/factory.js
index 0ad2e9d7b822..1009bcbe71a6 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/factory.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/factory.js
@@ -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' );
 
 
@@ -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;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/main.js
index 72e11be3a76f..1cd8d0b216b9 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/lib/main.js
@@ -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' );
 
 
@@ -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 );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/manifest.json
index 2e552b6f15a9..deead4e9c63b 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/manifest.json
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/manifest.json
@@ -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"
       ]
     },
@@ -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"
       ]
@@ -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"
       ]
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/src/main.c
index 1bda2b4b87f2..e1f7b94207ab 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/src/main.c
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/src/main.c
@@ -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"
 
 /**
@@ -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 );
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.factory.js
index dfdd21d01249..43b17c3a572e 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.factory.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.factory.js
@@ -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' );
@@ -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;
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.logpdf.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.logpdf.js
index 5dd308cc1843..5617ac3a9ebb 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.logpdf.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.logpdf.js
@@ -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' );
@@ -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;
 
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.native.js
index 40a28551a640..294348bca821 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/logpdf/test/test.native.js
@@ -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' );
@@ -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;
 
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.factory.js
index 83f5bdca0822..f12f4d466734 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.factory.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.factory.js
@@ -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;
 
@@ -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();
 });
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.native.js
index b68ba162c2c3..18ac65742304 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.native.js
@@ -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 );
@@ -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();
 });
 
diff --git a/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.pdf.js b/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.pdf.js
index 6732924525c0..713bba4af22b 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.pdf.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/betaprime/pdf/test/test.pdf.js
@@ -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 );
@@ -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();
 });