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/cdf/README.md

@@ -39,7 +39,7 @@ F(x;c)=\frac{\ln(1+cx)}{\ln(1+c)}
 
 <!-- </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>
 
@@ -66,6 +66,12 @@ y = cdf( 0.5, 5.0 );
 
 y = cdf( 1.0, 10.0 );
 // returns 1.0
+
+y = cdf( -0.5, 1.0 );
+// returns 0.0
+
+y = cdf( 2.0, 1.0 );
+// returns 1.0
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.
@@ -78,23 +84,13 @@ y = cdf( 0.0, NaN );
 // returns NaN
 ```
 
-If provided an input value `x` outside of the interval `[0,1]`, the function returns `NaN`.
-
-```javascript
-var y = cdf( 2.0, 1.0 );
-// returns NaN
-
-y = cdf( -0.5, 1.0 );
-// returns NaN
-```
-
 If provided a shape parameter `c <= 0`, the function returns `NaN`.
 
 ```javascript
 var y = cdf( 0.0, 0.0 );
 // returns NaN
 
-y = cdf( 0.5, -1.0 );
+y = cdf( 0.5, -5.0 );
 // returns NaN
 ```
 

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

@@ -6,8 +6,6 @@
 
     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
@@ -31,12 +29,16 @@
     ~0.699
     > y = {{alias}}( 1.0, 10.0 )
     1.0
-    > y = {{alias}}( 0.5, 0.0 )
-    NaN
+    > y = {{alias}}( -1.0, 0.5 )
+    0.0
     > y = {{alias}}( 2.0, 0.5 )
+    1.0
+
+    > y = {{alias}}( 0.5, 0.0 )
     NaN
-    > y = {{alias}}( -1.0, 0.5 )
+    > 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/cdf/docs/types/index.d.ts

@@ -36,8 +36,6 @@ interface CDF {
 	*
 	* ## 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 CDF {
 	* // returns 1.0
 	*
 	* @example
-	* var y = cdf( 0.5, 0.0 );
-	* // returns NaN
+	* var y = cdf( -1.0, 0.5 );
+	* // returns 0.0
 	*
 	* @example
 	* var y = cdf( 2.0, 0.5 );
+	* // returns 1.0
+	*
+	* @example
+	* var y = cdf( 0.5, 0.0 );
 	* // returns NaN
 	*
 	* @example
-	* var y = cdf( -1.0, 0.5 );
+	* var y = cdf( 0.5, -5.0 );
 	* // returns NaN
 	*
 	* @example

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

@@ -30,7 +30,7 @@ var log1p = require( '@stdlib/math/base/special/log1p' );
 /**
 * Returns a function for evaluating the cumulative distribution function (CDF) for a Bradford distribution with shape parameter `c`.
 *
-* @param {number} c - shape parameter
+* @param {PositiveNumber} c - shape parameter
 * @returns {Function} CDF
 *
 * @example
@@ -55,20 +55,24 @@ function factory( c ) {
 	*
 	* @private
 	* @param {number} x - input value
-	* @returns {number} evaluated CDF
+	* @returns {Probability} evaluated CDF
 	*
 	* @example
 	* var y = cdf( 0.5 );
 	* // returns <number>
 	*/
 	function cdf( x ) {
 		if (
-			isnan( x ) ||
-			x < 0.0 ||
-			x > 1.0
+			isnan( x )
 		) {
 			return NaN;
 		}
+		if ( x <= 0.0 ) {
+			return 0.0;
+		}
+		if ( x >= 1.0 ) {
+			return 1.0;
+		}
 		return log1p( c * x ) / log1p( c );
 	}
 }

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

@@ -30,8 +30,8 @@ var log1p = require( '@stdlib/math/base/special/log1p' );
 * Returns the cumulative distribution function (CDF) 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 CDF
+* @param {PositiveNumber} c - shape parameter
+* @returns {Probability} evaluated CDF
 *
 * @example
 * var v = cdf( 0.1, 0.1 );
@@ -46,15 +46,19 @@ var log1p = require( '@stdlib/math/base/special/log1p' );
 * // returns 1.0
 *
 * @example
-* var v = cdf( 0.5, 0.0 );
-* // returns NaN
+* var v = cdf( -1.0, 0.5 );
+* // returns 0.0
 *
 * @example
 * var v = cdf( 2.0, 0.5 );
+* // returns 1.0
+*
+* @example
+* var v = cdf( 0.5, 0.0 );
 * // returns NaN
 *
 * @example
-* var v = cdf( -1.0, 0.5 );
+* var v = cdf( 0.5, -5.0 );
 * // returns NaN
 *
 * @example
@@ -69,12 +73,16 @@ function cdf( 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 ) {
+		return 0.0;
+	}
+	if ( x >= 1.0 ) {
+		return 1.0;
+	}
 	return log1p( c * x ) / log1p( c );
 }
 

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

@@ -71,20 +71,38 @@ 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 greater than or equal to one for `x` and a finite `c`, the function returns `1`', function test( t ) {
 	var y;
 
-	y = cdf( 2.0, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( PINF, 0.5 );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( -0.5, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( 100.0, 0.5 );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( NINF, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( 10.0, 0.5 );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( PINF, 1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( 1.0, 0.5 );
+	t.equal( y, 1.0, 'returns 1' );
+
+	t.end();
+});
+
+tape( 'if provided a number less than or equal to zero for `x` and a finite `c`, the function returns `0`', function test( t ) {
+	var y;
+
+	y = cdf( NINF, 0.5 );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( -100.0, 0.5 );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( -1.0, 0.5 );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( 0.0, 0.5 );
+	t.equal( y, 0.0, 'returns 0' );
 
 	t.end();
 });

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

@@ -23,6 +23,8 @@
 var tape = require( 'tape' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var abs = require( '@stdlib/math/base/special/abs' );
+var PINF = require( '@stdlib/constants/float64/pinf' );
+var NINF = require( '@stdlib/constants/float64/ninf' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 var factory = require( './../lib/factory.js' );
 
@@ -72,7 +74,6 @@ tape( 'if provided `c <= 0`, the created function always returns `NaN`', functio
 	var y;
 
 	cdf = factory( -1.0 );
-
 	y = cdf( 1.0 );
 	t.equal( isnan( y ), true, 'returns expected value' );
 
@@ -85,23 +86,45 @@ 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 finite `c`, the function returns a function which returns `1` when provided a number greater than or equal to one for `x`', function test( t ) {
 	var cdf;
 	var y;
 
-	cdf = factory( 1.0 );
+	cdf = factory( 0.5 );
+	y = cdf( PINF );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( -1.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( 100.0 );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( -0.5 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( 10.0 );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( 1.5 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	y = cdf( 1.0 );
+	t.equal( y, 1.0, 'returns 1' );
 
-	y = cdf( 10.0 );
-	t.equal( isnan( y ), true, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if provided a finite `c`, the function returns a function which returns `0` when provided a number smaller than or equal to zero for `x`', function test( t ) {
+	var cdf;
+	var y;
+
+	cdf = factory( 0.5 );
+	y = cdf( NINF );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( -100.0 );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( -10.0 );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( -1.0 );
+	t.equal( y, 0.0, 'returns 0' );
+
+	y = cdf( 0.0 );
+	t.equal( y, 0.0, 'returns 0' );
 
 	t.end();
 });