From 67d2396e63786e164cc094d8320e0f06b0c32994 Mon Sep 17 00:00:00 2001 From: Sajal Kumar Jana Date: Fri, 2 Oct 2026 01:56:24 +0000 Subject: [PATCH 1/2] fix: return MGF for number of failures in `stats/base/dists/geometric/mgf` The geometric distribution in stdlib models the number of failures before the first success (support 0, 1, 2, ...), as documented by `pmf`, `cdf`, `mean`, and `variance`. Its MGF is therefore `p / (1 - (1-p) e^t)`. The implementation returned `p e^t / (1 - (1-p) e^t)`, which is the MGF of the number of trials (support 1, 2, ...), so every value was off by a factor of `e^t`. For example, `mgf( 0.5, 1.0 )` returned `e^0.5` instead of `1`, and the derivative at `t = 0` was `1/p` instead of `mean( p ) = (1-p)/p`. This commit fixes the JavaScript and C implementations, regenerates the test fixtures, updates the `p = 1` test, and corrects the documented equation and examples, including those in `geometric/ctor`. --- .../stats/base/dists/geometric/ctor/README.md | 2 +- .../stats/base/dists/geometric/ctor/docs/repl.txt | 2 +- .../stats/base/dists/geometric/ctor/lib/main.js | 2 +- .../stats/base/dists/geometric/mgf/README.md | 14 +++++++------- .../stats/base/dists/geometric/mgf/docs/repl.txt | 6 +++--- .../base/dists/geometric/mgf/docs/types/index.d.ts | 12 ++++++------ .../stats/base/dists/geometric/mgf/lib/factory.js | 4 ++-- .../stats/base/dists/geometric/mgf/lib/index.js | 6 +++--- .../stats/base/dists/geometric/mgf/lib/main.js | 6 +++--- .../stats/base/dists/geometric/mgf/lib/native.js | 4 ++-- .../stats/base/dists/geometric/mgf/src/main.c | 4 ++-- .../geometric/mgf/test/fixtures/julia/large_p.json | 2 +- .../geometric/mgf/test/fixtures/julia/small_p.json | 2 +- .../base/dists/geometric/mgf/test/test.mgf.js | 8 +++++--- .../base/dists/geometric/mgf/test/test.native.js | 8 +++++--- 15 files changed, 43 insertions(+), 39 deletions(-) diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/README.md b/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/README.md index e4b606ca771a..d4a18f0b01ac 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/README.md +++ b/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 ) diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/docs/repl.txt index 51f0d48c55d2..5aed6fad819a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/docs/repl.txt +++ b/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 ) diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/lib/main.js index 182bcb99e07a..4d430c2f0aa0 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/ctor/lib/main.js +++ b/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 ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/README.md b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/README.md index 59cb483c5f20..9b8f74caa8e5 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/README.md +++ b/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 - + ```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) ``` - @@ -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 ``` @@ -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: diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/repl.txt index 5a6d230e486d..6d4f26b13c98 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/repl.txt +++ b/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 -------- diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/types/index.d.ts index 5d32752c6f8e..6f99c7983988 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/docs/types/index.d.ts +++ b/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; diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/factory.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/factory.js index d9d74dae0a1f..d1d05b8af00b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/factory.js +++ b/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) ); } } diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/index.js index 1decc320a1f1..d9a9c3c5e758 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/index.js +++ b/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 // diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/main.js index 8126d1911512..441c2fa6d298 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/main.js +++ b/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) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/native.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/native.js index d53f5be5492c..a706a9b90e3a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/lib/native.js +++ b/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) diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/src/main.c index e9d0ddd26b07..3d333b0ba78c 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/src/main.c +++ b/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 ) ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json index c791b8fa41eb..16dea244d087 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json index ad574cb277d0..d4c75869575a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/test.mgf.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/test.mgf.js index 24fe800969af..dc4916a8c16b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/test.mgf.js +++ b/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(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/test.native.js index 31c3739b443d..91299bb6fe68 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/test.native.js +++ b/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(); }); From 76ef948b2d639cc3c2bf1e4b131e295d555c786f Mon Sep 17 00:00:00 2001 From: Sajal Kumar Jana Date: Fri, 2 Oct 2026 15:24:34 +0000 Subject: [PATCH 2/2] test: regenerate fixtures with Distributions.jl 0.25 in `stats/base/dists/geometric/mgf` --- .../base/dists/geometric/mgf/test/fixtures/julia/REQUIRE | 6 +++--- .../dists/geometric/mgf/test/fixtures/julia/large_p.json | 2 +- .../dists/geometric/mgf/test/fixtures/julia/small_p.json | 2 +- 3 files changed, 5 insertions(+), 5 deletions(-) diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/REQUIRE index 98be20b58ed3..1bdd5c67a9b9 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/REQUIRE +++ b/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 diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json index 16dea244d087..95d62f470ecf 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/large_p.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json index d4c75869575a..2abb5c39e827 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json +++ b/lib/node_modules/@stdlib/stats/base/dists/geometric/mgf/test/fixtures/julia/small_p.json @@ -1 +1 @@ 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