fix: handle negative t in stats/base/dists/weibull/mgf

lib/node_modules/@stdlib/stats/base/dists/weibull/ctor/docs/repl.txt

@@ -95,7 +95,7 @@
     > weibull.logpdf( 1.0 )
     ~-7.865
     > weibull.mgf( -0.5 )
-    ~0.075
+    ~0.109
     > weibull.pdf( 3.0 )
     ~0.089
     > weibull.quantile( 0.8 )

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/README.md

@@ -66,7 +66,7 @@ var y = mgf( 1.0, 1.0, 0.5);
 // returns ~2.0
 
 y = mgf( -1.0, 4.0, 4.0 );
-// returns ~0.019
+// returns ~0.045
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/docs/repl.txt

@@ -28,7 +28,7 @@
     > var y = {{alias}}( 1.0, 1.0, 0.5 )
     ~2.0
     > y = {{alias}}( -1.0, 4.0, 4.0 )
-    ~0.019
+    ~0.045
 
     > y = {{alias}}( NaN, 1.0, 1.0 )
     NaN

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/docs/types/index.d.ts

@@ -48,7 +48,7 @@ interface MGF {
 	*
 	* @example
 	* var y = mgf( -1.0, 4.0, 4.0 );
-	* // returns ~0.019
+	* // returns ~0.045
 	*
 	* @example
 	* var y = mgf( NaN, 1.0, 1.0 );
@@ -112,7 +112,7 @@ interface MGF {
 * // returns ~2.0
 *
 * y = mgf( -1.0, 4.0, 4.0 );
-* // returns ~0.019
+* // returns ~0.045
 *
 * var myMGF = mgf.factory( 8.0, 10.0 );
 *

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/lib/factory.js

@@ -23,6 +23,7 @@
 var constantFunction = require( '@stdlib/utils/constant-function' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var gamma = require( '@stdlib/math/base/special/gamma' );
+var abs = require( '@stdlib/math/base/special/abs' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 
 
@@ -87,7 +88,7 @@ function factory( k, lambda ) {
 				summand = c * gamma( 1.0 + (n / k) );
 			}
 			sum += summand;
-		} while ( summand / sum > EPS );
+		} while ( abs( summand / sum ) > EPS );
 		return sum;
 	}
 }

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/lib/index.js

@@ -30,7 +30,7 @@
 * // returns ~2.0
 *
 * y = mgf( -1.0, 4.0, 4.0 );
-* // returns ~0.019
+* // returns ~0.045
 *
 * var myMGF = mgf.factory( 8.0, 10.0 );
 *

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/lib/main.js

@@ -22,6 +22,7 @@
 
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
 var gamma = require( '@stdlib/math/base/special/gamma' );
+var abs = require( '@stdlib/math/base/special/abs' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 
 
@@ -41,7 +42,7 @@ var EPS = require( '@stdlib/constants/float64/eps' );
 *
 * @example
 * var y = mgf( -1.0, 4.0, 4.0 );
-* // returns ~0.019
+* // returns ~0.045
 *
 * @example
 * var y = mgf( NaN, 1.0, 1.0 );
@@ -98,7 +99,7 @@ function mgf( t, k, lambda ) {
 			summand = c * gamma( 1.0 + (n / k) );
 		}
 		sum += summand;
-	} while ( summand / sum > EPS );
+	} while ( abs( summand / sum ) > EPS );
 	return sum;
 }
 

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/lib/native.js

@@ -40,7 +40,7 @@ var addon = require( './../src/addon.node' );
 *
 * @example
 * var y = mgf( -1.0, 4.0, 4.0 );
-* // returns ~0.019
+* // returns ~0.045
 *
 * @example
 * var y = mgf( NaN, 1.0, 1.0 );

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/manifest.json

@@ -41,6 +41,7 @@
         "@stdlib/math/base/napi/ternary",
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/special/gamma",
+        "@stdlib/math/base/special/abs",
         "@stdlib/constants/float64/eps"
       ]
     },
@@ -58,6 +59,7 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/special/gamma",
+        "@stdlib/math/base/special/abs",
         "@stdlib/constants/float64/eps"
       ]
     },
@@ -75,6 +77,7 @@
       "dependencies": [
         "@stdlib/math/base/assert/is-nan",
         "@stdlib/math/base/special/gamma",
+        "@stdlib/math/base/special/abs",
         "@stdlib/constants/float64/eps"
       ]
     }

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/src/main.c

@@ -19,6 +19,7 @@
 #include "stdlib/stats/base/dists/weibull/mgf.h"
 #include "stdlib/math/base/assert/is_nan.h"
 #include "stdlib/math/base/special/gamma.h"
+#include "stdlib/math/base/special/abs.h"
 #include "stdlib/constants/float64/eps.h"
 
 /**
@@ -60,6 +61,6 @@ double stdlib_base_dists_weibull_mgf( const double t, const double k, const doub
 			summand = c * stdlib_base_gamma( 1.0 + (n / k) );
 		}
 		sum += summand;
-	} while ( summand / sum > STDLIB_CONSTANT_FLOAT64_EPS );
+	} while ( stdlib_base_abs( summand / sum ) > STDLIB_CONSTANT_FLOAT64_EPS );
 	return sum;
 }

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/test/test.factory.js

@@ -23,6 +23,7 @@
 var tape = require( 'tape' );
 var isNumber = require( '@stdlib/assert/is-number' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var randu = require( '@stdlib/random/base/randu' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
@@ -163,7 +164,7 @@
 	var x;
 	var y;
 
 	// TODO: Add test fixtures (function is not available in R and Julia)
 	mgf = factory( 2.0, 2.0 );
 	for ( i = 0; i < 100; i++ ) {
 		x = randu();
@@ -172,3 +173,28 @@
 	}
 	t.end();
 });
+
+tape( 'the created function evaluates the mgf for negative `t`', function test( t ) {
+	var expected;
+	var mgf;
+	var x;
+	var y;
+	var i;
+
+	// Reference values computed by summing the series in 1024-bit precision:
+	mgf = factory( 2.0, 4.0 );
+	x = [ -0.3 ];
+	expected = [ 0.39615540526349546 ];
+	for ( i = 0; i < x.length; i++ ) {
+		y = mgf( x[ i ] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' );
+	}
+	mgf = factory( 1.0, 1.0 );
+	x = [ -0.1, -0.5 ];
+	expected = [ 0.9090909090909091, 0.6666666666666666 ];
+	for ( i = 0; i < x.length; i++ ) {
+		y = mgf( x[ i ] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' );
+	}
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/test/test.mgf.js

@@ -23,6 +23,7 @@
 var tape = require( 'tape' );
 var isNumber = require( '@stdlib/assert/is-number' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var randu = require( '@stdlib/random/base/randu' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
@@ -124,7 +125,7 @@
 	var x;
 	var y;
 
 	// TODO: Add test fixtures (function is not available in R and Julia)
 	for ( i = 0; i < 100; i++ ) {
 		x = randu() * 5.0;
 		lambda = (randu() * 10.0) + EPS;
@@ -134,3 +135,30 @@
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the mgf for negative `t`', function test( t ) {
+	var expected;
+	var lambda;
+	var k;
+	var x;
+	var y;
+	var i;
+
+	// Reference values computed by summing the series in 1024-bit precision:
+	x = [ -0.1, -0.5, -0.2, -0.3, -2.0, -0.5 ];
+	k = [ 1.0, 1.0, 3.0, 2.0, 2.0, 1.5 ];
+	lambda = [ 1.0, 1.0, 0.5, 4.0, 1.0, 2.0 ];
+	expected = [
+		0.9090909090909091,
+		0.6666666666666666,
+		0.9150539469807932,
+		0.39615540526349546,
+		0.2421278438586879,
+		0.4728095755272915
+	];
+	for ( i = 0; i < x.length; i++ ) {
+		y = mgf( x[ i ], k[ i ], lambda[ i ] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' );
+	}
+	t.end();
+});

lib/node_modules/@stdlib/stats/base/dists/weibull/mgf/test/test.native.js

@@ -25,6 +25,7 @@
 var tryRequire = require( '@stdlib/utils/try-require' );
 var isNumber = require( '@stdlib/assert/is-number' );
 var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
 var randu = require( '@stdlib/random/base/randu' );
 var PINF = require( '@stdlib/constants/float64/pinf' );
 var NINF = require( '@stdlib/constants/float64/ninf' );
@@ -118,7 +119,7 @@
 	var x;
 	var y;
 
 	// TODO: Add test fixtures (function is not available in R and Julia)
 	for ( i = 0; i < 100; i++ ) {
 		x = randu() * 5.0;
 		lambda = (randu() * 10.0) + EPS;
@@ -128,3 +129,30 @@
 	}
 	t.end();
 });
+
+tape( 'the function evaluates the mgf for negative `t`', opts, function test( t ) {
+	var expected;
+	var lambda;
+	var k;
+	var x;
+	var y;
+	var i;
+
+	// Reference values computed by summing the series in 1024-bit precision:
+	x = [ -0.1, -0.5, -0.2, -0.3, -2.0, -0.5 ];
+	k = [ 1.0, 1.0, 3.0, 2.0, 2.0, 1.5 ];
+	lambda = [ 1.0, 1.0, 0.5, 4.0, 1.0, 2.0 ];
+	expected = [
+		0.9090909090909091,
+		0.6666666666666666,
+		0.9150539469807932,
+		0.39615540526349546,
+		0.2421278438586879,
+		0.4728095755272915
+	];
+	for ( i = 0; i < x.length; i++ ) {
+		y = mgf( x[ i ], k[ i ], lambda[ i ] );
+		t.strictEqual( isAlmostSameValue( y, expected[ i ], 4 ), true, 'returns expected value' );
+	}
+	t.end();
+});