fix: return MGF for number of failures in stats/base/dists/geometric/mgf

lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/README.md

@@ -224,7 +224,7 @@ Evaluates the [moment-generating function][mgf] (MGF).
 var geometric = new Geometric( 0.2 );
 
 var y = geometric.mgf( 0.1 );
-// returns ~1.908
+// returns ~1.726
 ```
 
 #### Geometric.prototype.pmf( x )

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

@@ -86,7 +86,7 @@
     > geometric.logpmf( 4.0 )
     ~-4.176
     > geometric.mgf( 0.5 )
-    ~2.905
+    ~1.762
     > geometric.pmf( 2.0 )
     ~0.096
     > geometric.quantile( 0.7 )

lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/lib/main.js

@@ -375,7 +375,7 @@ setReadOnly( Geometric.prototype, 'logpmf', geometricLogPMF );
 * var geometric = new Geometric( 0.2 );
 *
 * var v = geometric.mgf( 0.1 );
-* // returns ~1.908
+* // returns ~1.726
 */
 setReadOnly( Geometric.prototype, 'mgf', geometricMGF );
 

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

@@ -28,13 +28,13 @@ limitations under the License.
 
 The [moment-generating function][mgf] for a [geometric][geometric-distribution] random variable is
 
-<!-- <equation class="equation" label="eq:geometric_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{pe^t}{1-(1-p) e^t} \text{ for } t<-\ln(1-p)" alt="Moment-generating function (MGF) for a geometric distribution."> -->
+<!-- <equation class="equation" label="eq:geometric_mgf_function" align="center" raw="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{p}{1-(1-p) e^t} \text{ for } t<-\ln(1-p)" alt="Moment-generating function (MGF) for a geometric distribution."> -->
 
 ```math
-M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{pe^t}{1-(1-p) e^t} \text{ for } t<-\ln(1-p)
+M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{p}{1-(1-p) e^t} \text{ for } t<-\ln(1-p)
 ```
 
-<!-- <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{pe^t}{1-(1-p) e^t} \text{ for } t&lt;-\ln(1-p)" data-equation="eq:geometric_mgf_function">
+<!-- <div class="equation" align="center" data-raw-text="M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \frac{p}{1-(1-p) e^t} \text{ for } t&lt;-\ln(1-p)" data-equation="eq:geometric_mgf_function">
     <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/img/equation_geometric_mgf_function.svg" alt="Moment-generating function (MGF) for a geometric distribution.">
     <br>
 </div> -->
@@ -63,10 +63,10 @@ Evaluates the moment-generating function ([MGF][mgf]) of a [geometric][geometric
 
 ```javascript
 var y = mgf( 0.2, 0.5 );
-// returns ~1.569
+// returns ~1.284
 
 y = mgf( 0.4, 0.5 );
-// returns ~2.936
+// returns ~1.968
 ```
 
 If provided `NaN` as any argument, the function returns `NaN`.
@@ -103,7 +103,7 @@ Returns a function for evaluating the [moment-generating function][mgf] of a [ge
 ```javascript
 var mymgf = mgf.factory( 0.8 );
 var y = mymgf( -0.2 );
-// returns ~0.783
+// returns ~0.957
 ```
 
 </section>
@@ -176,7 +176,7 @@ Evaluates the [moment-generating function][mgf] of a [geometric][geometric-distr
 
 ```c
 double out = stdlib_base_dists_geometric_mgf( 0.2, 0.5 );
-// returns ~1.569
+// returns ~1.284
 ```
 
 The function accepts the following arguments:

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

@@ -25,9 +25,9 @@
     Examples
     --------
     > var y = {{alias}}( 0.2, 0.5 )
-    ~1.569
+    ~1.284
     > y = {{alias}}( 0.4, 0.5 )
-    ~2.936
+    ~1.968
     // Case: t >= -ln(1-p)
     > y = {{alias}}( 0.8, 0.5 )
     NaN
@@ -59,7 +59,7 @@
     --------
     > var mymgf = {{alias}}.factory( 0.8 );
     > var y = mymgf( -0.2 )
-    ~0.783
+    ~0.957
 
     See Also
     --------

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

@@ -43,11 +43,11 @@ interface MGF {
 	*
 	* @example
 	* var y = mgf( 0.2, 0.5 );
-	* // returns ~1.569
+	* // returns ~1.284
 	*
 	* @example
 	* var y = mgf( 0.4, 0.5 );
-	* // returns ~2.936
+	* // returns ~1.968
 	*
 	* @example
 	* // Case: t >= -ln(1-p)
@@ -81,7 +81,7 @@ interface MGF {
 	* @example
 	* var mymgf = mgf.factory( 0.8 );
 	* var y = mymgf( -0.2 );
-	* // returns ~0.783
+	* // returns ~0.957
 	*/
 	factory( p: number ): Unary;
 }
@@ -95,14 +95,14 @@ interface MGF {
 *
 * @example
 * var y = mgf( 0.2, 0.5 );
-* // returns ~1.569
+* // returns ~1.284
 *
 * y = mgf( 0.4, 0.5 );
-* // returns ~2.936
+* // returns ~1.968
 *
 * var mymgf = mgf.factory( 0.8 );
 * y = mymgf( -0.2 );
-* // returns ~0.783
+* // returns ~0.957
 */
 declare var mgf: MGF;
 

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

@@ -38,7 +38,7 @@ var ln = require( '@stdlib/math/base/special/ln' );
 * @example
 * var mgf = factory( 0.8 );
 * var y = mgf( -0.2 );
-* // returns ~0.783
+* // returns ~0.957
 */
 function factory( p ) {
 	if ( !isProbability( p ) ) {
@@ -68,7 +68,7 @@ function factory( p ) {
 			return NaN;
 		}
 		et = exp( t );
-		return ( p * et ) / ( 1.0 - (q * et ));
+		return p / ( 1.0 - (q * et) );
 	}
 }
 

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

@@ -27,14 +27,14 @@
 * var mgf = require( '@stdlib/stats/base/dists/geometric/mgf' );
 *
 * var y = mgf( 0.2, 0.5 );
-* // returns ~1.569
+* // returns ~1.284
 *
 * y = mgf( 0.4, 0.5 );
-* // returns ~2.936
+* // returns ~1.968
 *
 * var mymgf = mgf.factory( 0.8 );
 * y = mymgf( -0.2 );
-* // returns ~0.783
+* // returns ~0.957
 */
 
 // MODULES //

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

@@ -37,11 +37,11 @@ var ln = require( '@stdlib/math/base/special/ln' );
 *
 * @example
 * var y = mgf( 0.2, 0.5 );
-* // returns ~1.569
+* // returns ~1.284
 *
 * @example
 * var y = mgf( 0.4, 0.5 );
-* // returns ~2.936
+* // returns ~1.968
 *
 * @example
 * // Case: t >= -ln(1-p)
@@ -75,7 +75,7 @@ function mgf( t, p ) {
 		return NaN;
 	}
 	et = exp( t );
-	return ( p * et ) / ( 1.0 - (q * et) );
+	return p / ( 1.0 - (q * et) );
 }
 
 

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

@@ -35,11 +35,11 @@ var addon = require( './../src/addon.node' );
 *
 * @example
 * var y = mgf( 0.2, 0.5 );
-* // returns ~1.569
+* // returns ~1.284
 *
 * @example
 * var y = mgf( 0.4, 0.5 );
-* // returns ~2.936
+* // returns ~1.968
 *
 * @example
 * // Case: t >= -ln(1-p)

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

@@ -30,7 +30,7 @@
 *
 * @example
 * double y = stdlib_base_dists_geometric_mgf( 0.2, 0.5 );
-* // returns ~1.569
+* // returns ~1.284
 */
 double stdlib_base_dists_geometric_mgf( const double t, const double p ) {
 	if (
@@ -45,5 +45,5 @@ double stdlib_base_dists_geometric_mgf( const double t, const double p ) {
 	if ( t >= -stdlib_base_ln( q ) ) {
 		return 0.0/0.0; // NaN
 	}
-	return ( p * stdlib_base_exp( t ) ) / ( 1.0 - ( q * stdlib_base_exp( t ) ) );
+	return p / ( 1.0 - ( q * stdlib_base_exp( t ) ) );
 }

lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/REQUIRE

@@ -1,3 +1,3 @@
-Distributions 0.23.8
-julia 1.5
-JSON 0.21
+Distributions 0.25.131
+julia 1.10.10
+JSON 1.10.0

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

@@ -28,7 +28,6 @@ var NINF = require( '@stdlib/constants/float64/ninf' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 var isfinite = require( '@stdlib/math/base/assert/is-finite' );
 var ln = require( '@stdlib/math/base/special/ln' );
-var exp = require( '@stdlib/math/base/special/exp' );
 var mgf = require( './../lib' );
 
 
@@ -167,11 +166,14 @@ tape( 'the function returns `NaN` when `p` equals `0`', function test( t ) {
 	t.end();
 });
 
-tape( 'the function returns `e^t` when `p` equals `1`', function test( t ) {
+tape( 'the function returns `1` when `p` equals `1`', function test( t ) {
 	var y;
 
 	y = mgf( 0.5, 1.0 );
-	t.strictEqual( y, exp( 0.5 ), 'returns expected value' );
+	t.strictEqual( y, 1.0, 'returns expected value' );
+
+	y = mgf( -2.0, 1.0 );
+	t.strictEqual( y, 1.0, 'returns expected value' );
 	t.end();
 });
 

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

@@ -30,7 +30,6 @@ var NINF = require( '@stdlib/constants/float64/ninf' );
 var EPS = require( '@stdlib/constants/float64/eps' );
 var isfinite = require( '@stdlib/math/base/assert/is-finite' );
 var ln = require( '@stdlib/math/base/special/ln' );
-var exp = require( '@stdlib/math/base/special/exp' );
 
 
 // FIXTURES //
@@ -176,11 +175,14 @@ tape( 'the function returns `NaN` when `p` equals `0`', opts, function test( t )
 	t.end();
 });
 
-tape( 'the function returns `e^t` when `p` equals `1`', opts, function test( t ) {
+tape( 'the function returns `1` when `p` equals `1`', opts, function test( t ) {
 	var y;
 
 	y = mgf( 0.5, 1.0 );
-	t.strictEqual( y, exp( 0.5 ), 'returns expected value' );
+	t.strictEqual( y, 1.0, 'returns expected value' );
+
+	y = mgf( -2.0, 1.0 );
+	t.strictEqual( y, 1.0, 'returns expected value' );
 	t.end();
 });