diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/factory.js
index 8beaa7405647..5ae98175d721 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/factory.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/factory.js
@@ -23,7 +23,8 @@
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var ceil = require( '@stdlib/math/base/special/ceil' );
-var ln = require( '@stdlib/math/base/special/ln' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
+var max = require( '@stdlib/math/base/special/max' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
 
@@ -70,7 +71,7 @@ function factory( lambda ) {
 		if ( p === 1.0 ) {
 			return PINF;
 		}
-		return ceil( -ln( 1.0-p ) / lambda ) - 1.0;
+		return max( 0.0, ceil( -log1p( -p ) / lambda ) - 1.0 );
 	}
 }
 
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/main.js
index 90639967c5d1..b1a261e483f6 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/lib/main.js
@@ -22,7 +22,8 @@
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var ceil = require( '@stdlib/math/base/special/ceil' );
-var ln = require( '@stdlib/math/base/special/ln' );
+var log1p = require( '@stdlib/math/base/special/log1p' );
+var max = require( '@stdlib/math/base/special/max' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 
 
@@ -74,7 +75,7 @@ function quantile( p, lambda ) {
 	if ( p === 1.0 ) {
 		return PINF;
 	}
-	return ceil( -ln( 1.0-p ) / lambda ) - 1.0;
+	return max( 0.0, ceil( -log1p( -p ) / lambda ) - 1.0 );
 }
 
 
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/manifest.json
index 36f6fecd0dfc..60de0141d359 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/manifest.json
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/manifest.json
@@ -41,7 +41,8 @@
         "@stdlib/math/base/napi/binary",
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/special/ceil",
-        "@stdlib/math/base/special/ln",
+        "@stdlib/math/base/special/log1p",
+        "@stdlib/math/base/special/max",
         "@stdlib/constants/float64/pinf"
       ]
     },
@@ -59,7 +60,8 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/special/ceil",
-        "@stdlib/math/base/special/ln",
+        "@stdlib/math/base/special/log1p",
+        "@stdlib/math/base/special/max",
         "@stdlib/constants/float64/pinf"
       ]
     },
@@ -77,7 +79,8 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/special/ceil",
-        "@stdlib/math/base/special/ln",
+        "@stdlib/math/base/special/log1p",
+        "@stdlib/math/base/special/max",
         "@stdlib/constants/float64/pinf"
       ]
     }
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/src/main.c
index 91905928207d..713a964e60da 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/src/main.c
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/src/main.c
@@ -19,7 +19,8 @@
 #include "stdlib/stats/base/dists/planck/quantile.h"
 #include "stdlib/math/base/assert/is_nan.h"
 #include "stdlib/math/base/special/ceil.h"
-#include "stdlib/math/base/special/ln.h"
+#include "stdlib/math/base/special/log1p.h"
+#include "stdlib/math/base/special/max.h"
 #include "stdlib/constants/float64/pinf.h"
 
 /**
@@ -40,5 +41,5 @@ double stdlib_base_dists_planck_quantile( const double p, const double lambda )
 	if ( p == 1.0 ) {
 		return STDLIB_CONSTANT_FLOAT64_PINF;
 	}
-	return stdlib_base_ceil( -stdlib_base_ln( 1.0 - p ) / lambda ) - 1.0;
+	return stdlib_base_max( 0.0, stdlib_base_ceil( -stdlib_base_log1p( -p ) / lambda ) - 1.0 );
 }
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.factory.js b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.factory.js
index 44427a1e4fc6..b0c6a9b69372 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.factory.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.factory.js
@@ -146,3 +146,42 @@ tape( 'the returned function evaluates the quantile for `p` given large paramete
 	}
 	t.end();
 });
+
+tape( 'the returned function evaluates the quantile for small `p`', function test( t ) {
+	var quantile;
+	var y;
+
+	quantile = factory( 1.0 );
+	y = quantile( 1.0e-20 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-300 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	quantile = factory( 1.0e-17 );
+	y = quantile( 1.0e-15 );
+	t.strictEqual( y, 100.0, 'returns expected value' );
+
+	quantile = factory( 1.0e-14 );
+	y = quantile( 1.0e-12 );
+	t.strictEqual( y, 100.0, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the returned function returns `0` for `p = 0` and where `-ln(1-p)/lambda` underflows', function test( t ) {
+	var quantile;
+	var y;
+
+	quantile = factory( 1.0 );
+	y = quantile( 0.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	quantile = factory( 2.0 );
+	y = quantile( 5.0e-324 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	quantile = factory( 1.0e300 );
+	y = quantile( 1.0e-300 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+	t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.native.js
index 97e97b213345..137c8b765ae0 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.native.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.native.js
@@ -118,3 +118,34 @@ tape( 'the function evaluates the quantile for `p` given large parameter `lambda
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the quantile for small `p`', opts, function test( t ) {
+	var y;
+
+	y = quantile( 1.0e-20, 1.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-300, 1.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-15, 1.0e-17 );
+	t.strictEqual( y, 100.0, 'returns expected value' );
+
+	y = quantile( 1.0e-12, 1.0e-14 );
+	t.strictEqual( y, 100.0, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function returns `0` for `p = 0` and where `-ln(1-p)/lambda` underflows', opts, function test( t ) {
+	var y;
+
+	y = quantile( 0.0, 1.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 5.0e-324, 2.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-300, 1.0e300 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+	t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.quantile.js b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.quantile.js
index f7a0122742d3..eef4c3fcee9c 100644
--- a/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.quantile.js
+++ b/lib/node_modules/@stdlib/stats/base/dists/planck/quantile/test/test.quantile.js
@@ -109,3 +109,34 @@ tape( 'the function evaluates the quantile for `p` given large parameter `lambda
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the quantile for small `p`', function test( t ) {
+	var y;
+
+	y = quantile( 1.0e-20, 1.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-300, 1.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-15, 1.0e-17 );
+	t.strictEqual( y, 100.0, 'returns expected value' );
+
+	y = quantile( 1.0e-12, 1.0e-14 );
+	t.strictEqual( y, 100.0, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function returns `0` for `p = 0` and where `-ln(1-p)/lambda` underflows', function test( t ) {
+	var y;
+
+	y = quantile( 0.0, 1.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 5.0e-324, 2.0 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+
+	y = quantile( 1.0e-300, 1.0e300 );
+	t.strictEqual( y, 0.0, 'returns expected value' );
+	t.end();
+});