fix: update implementation to include support for x outside of [0,1]

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Author: anandkaranubc

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/README.md

@@ -39,7 +39,7 @@ f(x;c)=\frac{c}{(\ln(1+c)) (1 + cx)}
 
 <!-- </equation> -->
 
-where `c` is the shape parameter of the distribution. The parameters must satisfy `0 <= x <= 1` and `c > 0`.
+where `c > 0` is the shape parameter of the distribution.
 
 </section>
 
@@ -68,33 +68,33 @@ y = pdf( 1.0, 10.0 );
 // returns ~0.379
 ```
 
-If provided `NaN` as any argument, the function returns `NaN`.
+If provided a `x` outside the support `[0,1]`, the function returns `0`.
 
 ```javascript
-var y = pdf( NaN, 1.0 );
-// returns NaN
+var y = pdf( 2.0, 1.0 );
+// returns 0.0
 
-y = pdf( 0.0, NaN );
-// returns NaN
+y = pdf( -0.5, 1.0 );
+// returns 0.0
 ```
 
-If provided an input value `x` outside of the interval `[0,1]`, the function returns `NaN`.
+If provided `NaN` as any argument, the function returns `NaN`.
 
 ```javascript
-var y = pdf( 2.0, 1.0 );
+var y = pdf( NaN, 1.0 );
 // returns NaN
 
-y = pdf( -0.5, 1.0 );
+y = pdf( 0.0, NaN );
 // returns NaN
 ```
 
 If provided a shape parameter `c <= 0`, the function returns `NaN`.
 
 ```javascript
-var y = pdf( 0.0, 0.0 );
+var y = pdf( 0.5, 0.0 );
 // returns NaN
 
-y = pdf( 0.5, -1.0 );
+y = pdf( 0.5, -5.0 );
 // returns NaN
 ```
 

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/docs/repl.txt

@@ -5,8 +5,6 @@
 
     If provided `NaN` as any argument, the function returns `NaN`.
 
-    If `x < 0` or `x > 1`, the function returns `NaN`.
-
     If provided `c <= 0`, the function returns `NaN`.
 
     Parameters
@@ -30,12 +28,16 @@
     ~0.797
     > y = {{alias}}( 1.0, 10.0 )
     ~0.379
-    > y = {{alias}}( 0.5, 0.0 )
-    NaN
     > y = {{alias}}( 2.0, 0.5 )
-    NaN
+    0.0
     > y = {{alias}}( -1.0, 0.5 )
+    0.0
+
+    > y = {{alias}}( 0.5, 0.0 )
     NaN
+    > y = {{alias}}( 0.5, -5.0 )
+    NaN
+
     > y = {{alias}}( NaN, 1.0 )
     NaN
     > y = {{alias}}( 1.0, NaN )

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/docs/types/index.d.ts

@@ -36,8 +36,6 @@ interface PDF {
 	*
 	* ## Notes
 	*
-	* -   If `x < 0` or `x > 1`, the function returns `NaN`.
-	*
 	* -   If provided `c <= 0`, the function returns `NaN`.
 	*
 	* @param x - input value
@@ -57,15 +55,19 @@ interface PDF {
 	* // returns ~0.379
 	*
 	* @example
-	* var y = pdf( 0.5, 0.0 );
-	* // returns NaN
+	* var y = pdf( 2.0, 0.5 );
+	* // returns 0.0
 	*
 	* @example
-	* var y = pdf( 2.0, 0.5 );
+	* var y = pdf( -1.0, 0.5 );
+	* // returns 0.0
+	*
+	* @example
+	* var y = pdf( 0.5, 0.0 );
 	* // returns NaN
 	*
 	* @example
-	* var y = pdf( -1.0, 0.5 );
+	* var y = pdf( 0.5, -5.0 );
 	* // returns NaN
 	*
 	* @example

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/lib/factory.js

@@ -30,7 +30,7 @@ var log1p = require( '@stdlib/math/base/special/log1p' );
 /**
 * Returns a function for evaluating the probability density function (PDF) for a Bradford distribution with shape parameter `c`.
 *
-* @param {number} c - shape parameter
+* @param {PositiveNumber} c - shape parameter
 * @returns {Function} PDF
 *
 * @example
@@ -55,7 +55,7 @@ function factory( c ) {
 	*
 	* @private
 	* @param {number} x - input value
-	* @returns {number} evaluated PDF
+	* @returns {Probability} evaluated PDF
 	*
 	* @example
 	* var y = pdf( 0.5 );
@@ -64,12 +64,14 @@ function factory( c ) {
 	function pdf( x ) {
 		var k;
 		if (
-			isnan( x ) ||
-			x < 0.0 ||
-			x > 1.0
+			isnan( x )
 		) {
 			return NaN;
 		}
+		if ( x < 0.0 || x > 1.0 ) {
+			// Support of the Bradford distribution: [0,1]
+			return 0.0;
+		}
 		k = log1p( c );
 		return c / ( ( 1.0 + ( c * x ) ) * k );
 	}

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/lib/main.js

@@ -30,8 +30,8 @@ var log1p = require( '@stdlib/math/base/special/log1p' );
 * Returns the probability density function (PDF) for a Bradford distribution with shape parameter `c` at a value `x`.
 *
 * @param {number} x - input value
-* @param {number} c - shape parameter
-* @returns {number} evaluated PDF
+* @param {PositiveNumber} c - shape parameter
+* @returns {Probability} evaluated PDF
 *
 * @example
 * var v = pdf( 0.1, 0.1 );
@@ -46,15 +46,19 @@ var log1p = require( '@stdlib/math/base/special/log1p' );
 * // returns ~0.379
 *
 * @example
-* var v = pdf( 0.5, 0.0 );
-* // returns NaN
+* var v = pdf( 2.0, 0.5 );
+* // returns 0.0
 *
 * @example
-* var v = pdf( 2.0, 0.5 );
+* var v = pdf( -1.0, 0.5 );
+* // returns 0.0
+*
+* @example
+* var v = pdf( 0.5, 0.0 );
 * // returns NaN
 *
 * @example
-* var v = pdf( -1.0, 0.5 );
+* var v = pdf( 0.5, -5.0 );
 * // returns NaN
 *
 * @example
@@ -70,12 +74,14 @@ function pdf( x, c ) {
 	if (
 		isnan( c ) ||
 		isnan( x ) ||
-		c <= 0.0 ||
-		x < 0.0 ||
-		x > 1.0
+		c <= 0.0
 	) {
 		return NaN;
 	}
+	if ( x < 0.0 || x > 1.0 ) {
+		// Support of the Bradford distribution: [0,1]
+		return 0.0;
+	}
 	k = log1p( c );
 	return c / ( ( 1.0 + ( c * x ) ) * k );
 }

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/test/test.factory.js

@@ -72,7 +72,6 @@ tape( 'if provided `c <= 0`, the created function always returns `NaN`', functio
 	var y;
 
 	pdf = factory( -1.0 );
-
 	y = pdf( 1.0 );
 	t.equal( isnan( y ), true, 'returns expected value' );
 
@@ -85,23 +84,22 @@ tape( 'if provided `c <= 0`, the created function always returns `NaN`', functio
 	t.end();
 });
 
-tape( 'if provided a `x` outside of `[0,1]`, the created function always returns `NaN`', function test( t ) {
+tape( 'if provided a valid `c`, the function returns a function which returns `0` when provided a number outside [0,1] for `x`', function test( t ) {
 	var pdf;
 	var y;
 
 	pdf = factory( 1.0 );
-
 	y = pdf( -1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	y = pdf( -0.5 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	y = pdf( 1.5 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	y = pdf( 10.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	t.end();
 });

lib/node_modules/@stdlib/stats/base/dists/bradford/pdf/test/test.pdf.js

@@ -71,20 +71,20 @@ tape( 'if provided `c <= 0`, the function returns `NaN`', function test( t ) {
 	t.end();
 });
 
-tape( 'if provided a `x` outside of `[0,1]`, the created function always returns `NaN`', function test( t ) {
+tape( 'if provided a number outside [0,1] for `x` and a valid `c`, the function returns `0`', function test( t ) {
 	var y;
 
 	y = pdf( 2.0, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	y = pdf( -0.5, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	y = pdf( NINF, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	y = pdf( PINF, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.equal( y, 0.0, 'returns expected value' );
 
 	t.end();
 });