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fix: use expm1 in stats/base/dists/lognormal/variance #15774

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fix: use expm1 in stats/base/dists/lognormal/variance #15774

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74247b0
fix: use `expm1` in `stats/base/dists/lognormal/variance`
Abhist17 Oct 1, 2026
354c58a
test: generate `lognormal/stdev` fixtures in extended precision
Abhist17 Oct 1, 2026
08d946f
docs: move comment
kgryte Oct 2, 2026
b3f1feb
docs: move comment
kgryte Oct 2, 2026
ca457db
style: add semicolon
kgryte Oct 2, 2026
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1 change: 0 additions & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/stdev/test/fixtures/julia/REQUIRE
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@@ -1,3 +1,2 @@
Distributions 0.23.8
julia 1.5
JSON 0.21
2 changes: 1 addition & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/stdev/test/fixtures/julia/data.json
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@@ -1 +1 @@
{"sigma":[4.372448161181262,4.507779737981885,2.308292309093838,1.7741874189836637,0.31507521564566265,1.7945498757493117,2.484120101875779,1.8014970499175265,2.4955804577203144,2.185131411239958,2.805319026010679,0.8251792272092917,0.6749340206857746,0.6095685925273664,1.9222550510739178,3.610927283846249,4.363709627043577,0.8365430160947551,4.9582552039481005,3.944801044938724,1.4085253337087922,3.3578824067227595,0.8757806166602033,4.277911759657698,3.2398177086236357,2.6767355318357424,3.3005646996079396,4.075667020413391,2.1165984455816735,2.573158653777754,3.551529690803654,1.2656405632837509,1.49593156919257,2.3017718957908526,0.4823234640018226,1.1587034896771775,3.0831569181573784,1.1545926583806598,4.824989369186914,4.786962945045098,0.6786152774438026,3.760384015938966,4.197561605952372,1.6217772164357158,0.3640416335603147,1.010091708991523,0.9201385774137683,4.548798603750895,0.04081842516157064,4.36036983426966,4.42320519400549,2.9001714869597017,2.719448199461083,3.3350595840950925,0.9892978690118837,0.10336309764470086,3.9839675215599524,0.3181352586162056,3.762680927232196,0.5074452632699933,2.2006988264529337,2.3496823648832854,1.8428977548334557,0.05438641951580503,0.2733675289242188,0.12663328098316273,4.337325360579709,0.6957303538011506,2.4567548125520733,2.186112925258655,3.6404386228430505,3.7957019241094034,3.743686451322273,3.180827357760939,1.2192110149492374,3.8783824760250054,3.8717090528182863,0.6895675822024083,4.494831697610012,1.9754053512532177,0.43643372611896103,0.5541016454684644,4.333418678833584,4.434437046160502,2.546510808354628,4.153832150411521,2.91332028910133,1.5850106767162986,2.3151923474597047,2.271606850151444,3.683739031658267,2.1709264877425682,3.8551971556157505,3.8786127818556047,4.876192597625505,4.7692510203664185,4.456683646975332,2.5868300814009473,3.1274279753790735,0.052954852877593606],"expected":[3.7253726724275597e6,4.4392569855739765e7,10.26500714995574,0.7583755550911014,0.012537993106318921,0.5250924012496011,19.945929770815166,0.8873932670524205,58.99800429028618,3.0793004645544086,58.23330167244097,0.052983799885807085,0.017694546738403205,0.04276089588170603,0.8861449918044398,25583.978170436756,5.210435247142238e6,0.07726731625142313,2.282205332465917e9,300845.87106584816,0.8489915870937841,7565.624030014332,0.04688564423039902,2.8379738551656352e6,1628.5115935804004,26.04438879060696,2390.226993800247,1.7739110064637365e6,3.915078109264716,21.609887191480563,9902.176511368612,0.23019215723072528,1.1432560967366912,19.020885943664922,0.010549872754361192,0.29304804573033955,1112.5169174009964,0.06463114112942038,1.602215893135758e9,7.821441527583933e8,0.02053177262761622,43793.567353101695,4.00382637761903e6,0.7804898213066502,0.014548072766927071,0.15712050504826136,0.0899250239220967,1.0340983850597422e8,0.002763382281651077,1.3338991378090415e7,1.2029968926432032e7,91.86674114343772,159.76746685609865,2549.6102702632184,0.20540391898584445,0.002524152003730183,594826.9212999693,0.02660417850135068,138348.6954692866,0.07583186352353789,2.5705608582387764,5.481392903582849,2.1002074295351214,0.0045927964728261,0.025922792877743284,0.01222987029480063,1.347241934059741e7,0.0859996285048383,20.615755428435122,2.287552869097583,14659.7842284774,45355.90857710304,132266.81647678112,1381.6538970405961,0.09730611375029731,192589.6471404916,265528.09538348403,0.03066748818694898,3.4273557183928795e7,3.758030539779181,0.00980282677955075,0.028303354996340083,1.0851358083880417e7,1.1553346602298357e7,12.573809763433625,1.491836658643478e6,255.36686025510437,1.4931403273243335,16.442152836251903,9.241619100448267,59708.1223714079,2.986079715753444,214244.36162821326,255664.89844212984,5.993919604195529e8,1.7851854780063e8,8.4554828010827e6,16.592714898506497,389.34647776778627,0.002318327498523008],"mu":[-3.98762546864778,-2.7114954976045658,-2.997040364725514,-3.4023682391911962,-3.2987074965588783,-3.844211209781736,-3.176781759756721,-3.344992506860999,-2.1494304536902606,-3.6458590378443763,-3.805166363852011,-3.2659273608231563,-3.9873261256888033,-2.9386809425324363,-3.803359315774366,-2.8890731802426646,-3.575787755508017,-2.9170213642141847,-3.035886603959496,-2.947101840583809,-2.073674585671807,-2.343997804721533,-3.514844081636834,-3.4419280935348042,-3.100983223431985,-3.904723991270577,-3.1145744321206705,-2.222364355617197,-3.109454573305522,-3.5473281111037314,-3.4128516194375234,-2.958161607778441,-2.0475190459440453,-2.350109542871997,-3.998105101373435,-2.418670542756289,-2.4914391526522905,-3.919109563390459,-2.0858689714614504,-2.437464617091938,-3.847880314063043,-3.4532453645627728,-2.4167623683807977,-2.840597135985702,-3.3195702902127096,-2.6474993350078573,-2.975384923350693,-2.237358071496792,-2.693927848449905,-2.6066231020886623,-3.261832681743491,-3.890544375966013,-2.3213719533114814,-3.278919250986675,-2.3258485877939834,-3.7203581683573184,-2.5759713952532715,-2.5575292634904265,-2.3202348491098905,-2.0953764286339993,-3.8949942128965995,-3.817643045741262,-2.6372001083495875,-2.4738439837938335,-2.411858227645943,-2.3494463622077197,-2.3962361383427733,-2.458521389613533,-3.0083911887067365,-3.9473875144853188,-3.659929232021267,-3.6850570846183386,-2.222611337955388,-2.886605962629553,-3.688168467546199,-2.8735334599189004,-2.5006549004879934,-3.4741908662372865,-2.853627301762462,-2.5681294528080274,-3.939577155827911,-3.206601618579716,-2.5787166434288786,-3.401746212839236,-3.952337357226517,-3.0388029421093,-2.9446308968119768,-2.069096583162575,-2.5579115515060042,-2.933602031459561,-2.572709270933912,-3.614450892236255,-2.587672413853305,-2.5920140896284183,-3.56582794907076,-3.74555223216696,-3.911703486915384,-3.8821051553084347,-3.8163078417287046,-3.1306970243048586]}
{"expected":[33.296135828493554,0.22173877252337126,0.013167428204015966,245032.75895561316,656.814378786937,249951.5999778303,7.659955682026986,11.542903151272373,89305.9960918289,454801.3819156509,4696.100883668945,0.7408522314096593,1.3730765628719777e6,74756.42508083694,41.69754771144814,6.588056830372515e8,0.007544663341414214,0.0117661674868273,1.6171013514751928,0.11078470468761034,1054.3698135035088,3.944865302736056e8,1.2532263736746825,0.200132908362691,0.008124246222514637,1.2245906207901391e8,0.5014545211361671,0.15634630987068773,0.023430653313371057,0.1824216848250615,0.6357328391653366,0.00037864708785296966,99.5823145841211,0.012247956810828959,0.4360550521903704,0.17529754611163834,10.905280777310786,1.9843014279781194e9,4726.682196805757,0.020128826829171415,1.2340702762573578e6,30.03498339038285,0.05619076943734589,0.03765312415013708,0.00516382613215025,0.09040426942333746,0.034588226822355,1.757089130927487e7,0.10400255846462461,12.426307869652987,1.6387153683505628e7,5852.4972113960785,2306.2726180834024,1358.8184355829092,0.35996639831620353,571947.2853510635,1.324617877041741,0.528809567592436,0.12108900592447447,1.0124764325805196e6,3.6947881912426888,0.010463019668770472,1.8174734331538746e9,59463.658906825,1.3364736552839202e8,2.262519809022253,31535.96892722234,812.4005187630886,1.750794323895859e7,4.0530973042918006e6,1.0671320833196738e9,3.14167431418941,4493.122346608968,4.5177471019424087e8,0.8898387538115177,0.006470918617154905,5168.720751324912,1.1607244024862802e8,1.1882843293722134e7,7.394307476726226,0.011027608928167364,1.5163690677262183,0.0038385597786708514,168.8381925925224,1.2717574187343803,2.9091751459136534e8,1.5922412764745876e8,0.01445590562591941,0.07070948946021414,8.707662911813906e8,5535.651907696916,295496.4039345913,8.496806365375681e8,8.707300599794542e6,28384.691766091943,0.08320738369251311,0.14160488787951922,11728.89706046313,187.21173344773524,12.214834497197263],"mu":[-2.3915137116259975,-3.1019086374707423,-3.3190550833873314,-3.7088258654322095,-2.9518718244550994,-3.131055537176037,-3.327589575011668,-2.723841786480249,-3.724109634675675,-2.5341098033027567,-2.566209347269961,-3.3738514531109765,-3.8054077622439078,-2.4792978609967253,-2.2835116101237167,-2.6464174708053827,-3.5973283520267776,-2.7221774220364,-3.0933050409993728,-2.325939674630099,-3.6345212318142166,-3.413010024222376,-3.291322711128439,-3.190289164519498,-3.696232417534511,-3.7396300910070246,-2.3587732712529066,-2.7466091456069543,-2.2357697328227815,-3.3298066848676227,-2.289717533578983,-3.945205081002607,-3.257073029540999,-3.185457319678708,-3.9152786713896335,-3.209061556746237,-2.2248815112503513,-2.793505501911589,-2.8544004791848483,-3.649128852537258,-2.301913725278803,-2.086525471964408,-3.7821591417850784,-2.450640211173785,-3.6984440328453156,-2.001251938480629,-2.254563114488544,-3.491292699302009,-3.6626105657903265,-3.1955019645413754,-2.578588873202553,-2.712739911641811,-2.4791694243707973,-3.6452357146661445,-2.377459077233824,-3.8365797948488094,-2.4567483474873324,-2.8270893401321753,-3.0592780567354856,-2.7574761834137385,-2.4301906245644416,-3.4179554232063922,-2.8105562358070744,-2.477790083935151,-2.1636237495478063,-2.137028858732631,-3.5203955587819964,-2.373784346957203,-2.752073466682835,-2.7868760361941876,-3.720758122224696,-2.054555128690262,-2.9692149488619206,-2.3568130395485123,-2.1068007385665353,-2.6660652153851068,-3.8405500114502376,-2.304671537791454,-3.5403181738427656,-3.4361722233613623,-3.6169622365901306,-3.205766993715338,-3.7131714187797,-3.245084398315777,-3.9370099477013145,-3.1875578195908725,-2.818485597993085,-3.291298516224983,-3.889821333593931,-3.248648087946874,-3.0559437657810653,-2.336687533515765,-3.6522172047416004,-2.384723618028466,-3.0270043982458317,-2.8408411575174624,-2.5006360885689465,-2.322949779683995,-3.281349709225946,-3.5499631349619207],"sigma":[2.428647557746435,1.3026390303506012,0.33449597700119404,4.014719555093447,3.072346504486987,3.9446264972173335,2.31644939239025,2.2743691692118873,3.888950202804642,3.944835353964213,3.319744775013356,1.759833968269946,4.235324334303149,3.701525207710345,2.452585601164514,4.790861786091988,0.26158309524542567,0.17493834424797572,1.894191754702993,0.7439872519001911,3.2550318406702914,4.817271590655677,1.8793315356206426,1.2977545157191765,0.30522061887207463,4.728944642950482,1.3276497220544403,1.0462565353345699,0.21189646544084062,1.3139025632354047,1.3843137595736348,0.019565489946410386,2.803257199403109,0.27927421836600463,1.7629941145409718,1.2580757661760589,2.1492054451690477,4.919556714341288,3.3638349198923434,0.5929140546368278,4.040760101467751,2.34327858003246,1.0509227670634902,0.3894778813760663,0.20223163811526113,0.5375736317084284,0.30709595388205724,4.491441515603629,1.233834772459782,2.3910176375294516,4.380707380022288,3.37451764011574,3.197276264264819,3.2953931674312265,1.2182946530434058,4.134414338372601,1.664397989123389,1.4986306256818822,1.0679909735294557,4.072515931948811,1.9362399005757658,0.2985106625905809,4.912358841314619,3.6702740251795007,4.568844387655472,1.7261469420068343,3.7254905813830113,3.012280719247251,4.407974444547788,4.2428608222618625,4.950656392163446,1.7943535725047033,3.3733549771158544,4.720752823906282,1.4347036264419744,0.09247771305556873,3.520075651106116,4.568850684503092,4.453192602259016,2.3321790630038746,0.37024404143983225,1.9066852752897268,0.15452386655736672,2.893810741337581,2.0457464906858225,4.761943736501316,4.658788358966976,0.35364010706120885,1.176752020217583,4.881959879430762,3.416857128332323,3.8643368956882673,4.920628854108375,4.285369996214496,3.6442571956969765,0.8356964415533435,0.9119598432958065,3.4194685064654355,2.9178228717578,2.460445110772552]}
13 changes: 9 additions & 4 deletions lib/node_modules/@stdlib/stats/base/dists/lognormal/stdev/test/fixtures/julia/runner.jl
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Expand Up @@ -16,7 +16,6 @@
# See the License for the specific language governing permissions and
# limitations under the License.

import Distributions: var, LogNormal
import JSON

"""
Expand All @@ -39,9 +38,10 @@ julia> gen( mu, sigma, "data.json" );
```
"""
function gen( mu, sigma, name )
z = Array{Float64}( undef, length(mu) );
for i in eachindex(mu)
z[ i ] = sqrt( var( LogNormal( mu[i], sigma[i] ) ) );
# The standard deviation is evaluated in extended precision using the textbook formula `sqrt((exp(sigma^2) - 1) * exp(2*mu + sigma^2))`, as subtracting `1` from `exp(sigma^2)` in double-precision cancels for small `sigma`...
z = setprecision( BigFloat, 2048 ) do
s2 = BigFloat.( sigma ) .^ 2;
Float64.( sqrt.( ( exp.( s2 ) .- 1 ) .* exp.( ( 2 .* BigFloat.( mu ) ) .+ s2 ) ) );
end

# Store data to be written to file as a collection:
Expand Down Expand Up @@ -71,3 +71,8 @@ dir = dirname( file );
mu = rand( 100 ) .* 2.0 .- 4.0;
sigma = rand( 100 ) .* 5.0;
gen( mu, sigma, "data.json" );

# Small `sigma`:
mu = ( rand( 1000 ) .* 4.0 ) .- 2.0;
sigma = exp10.( range( -150.0, stop = -1.0, length = 1000 ) );
gen( mu, sigma, "small_sigma.json" );
1 change: 1 addition & 0 deletions ...ode_modules/@stdlib/stats/base/dists/lognormal/stdev/test/fixtures/julia/small_sigma.json
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22 changes: 21 additions & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/stdev/test/test.js
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Expand Up @@ -31,6 +31,7 @@ var stdev = require( './../lib' );
// FIXTURES //

var data = require( './fixtures/julia/data.json' );
var smallSigma = require( './fixtures/julia/small_sigma.json' );


// TESTS //
Expand Down Expand Up @@ -86,7 +87,26 @@ tape( 'the function returns the standard deviation of a lognormal distribution',
for ( i = 0; i < mu.length; i++ ) {
y = stdev( mu[i], sigma[i] );
if ( expected[i] !== null ) {
t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( y, expected[ i ], 18 ), true, 'returns expected value' );
}
}
t.end();
});

tape( 'the function returns the standard deviation of a lognormal distribution with a small `sigma`', function test( t ) {
var expected;
var sigma;
var mu;
var y;
var i;

expected = smallSigma.expected;
mu = smallSigma.mu;
sigma = smallSigma.sigma;
for ( i = 0; i < mu.length; i++ ) {
y = stdev( mu[i], sigma[i] );
if ( expected[i] !== null ) {
t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
}
}
t.end();
Expand Down
22 changes: 21 additions & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/stdev/test/test.native.js
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Expand Up @@ -32,6 +32,7 @@ var NINF = require( '@stdlib/constants/float64/ninf' );
// FIXTURES //

var data = require( './fixtures/julia/data.json' );
var smallSigma = require( './fixtures/julia/small_sigma.json' );


// VARIABLES //
Expand Down Expand Up @@ -98,7 +99,26 @@ tape( 'the function returns the standard deviation of a lognormal distribution',
for ( i = 0; i < mu.length; i++ ) {
y = stdev( mu[i], sigma[i] );
if ( expected[i] !== null ) {
t.strictEqual( isAlmostSameValue( y, expected[ i ], 0 ), true, 'returns expected value' );
t.strictEqual( isAlmostSameValue( y, expected[ i ], 18 ), true, 'returns expected value' );
}
}
t.end();
});

tape( 'the function returns the standard deviation of a lognormal distribution with a small `sigma`', opts, function test( t ) {
var expected;
var sigma;
var mu;
var y;
var i;

expected = smallSigma.expected;
mu = smallSigma.mu;
sigma = smallSigma.sigma;
for ( i = 0; i < mu.length; i++ ) {
y = stdev( mu[i], sigma[i] );
if ( expected[i] !== null ) {
t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' );
}
}
t.end();
Expand Down
3 changes: 2 additions & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/variance/lib/main.js
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Expand Up @@ -22,6 +22,7 @@

var isnan = require( '@stdlib/math/base/assert/is-nan' );
var exp = require( '@stdlib/math/base/special/exp' );
var expm1 = require( '@stdlib/math/base/special/expm1' );


// MAIN //
Expand Down Expand Up @@ -63,7 +64,7 @@ function variance( mu, sigma ) {
return NaN;
}
s2 = sigma*sigma;
return ( exp( s2 ) - 1.0 ) * exp( ( 2.0*mu ) + s2 );
return expm1( s2 ) * exp( ( 2.0*mu ) + s2 );
}


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3 changes: 3 additions & 0 deletions lib/node_modules/@stdlib/stats/base/dists/lognormal/variance/manifest.json
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Expand Up @@ -40,6 +40,7 @@
"dependencies": [
"@stdlib/math/base/napi/binary",
"@stdlib/math/base/assert/is-nan",
"@stdlib/math/base/special/expm1",
"@stdlib/math/base/special/exp"
]
},
Expand All @@ -56,6 +57,7 @@
"libpath": [],
"dependencies": [
"@stdlib/math/base/assert/is-nan",
"@stdlib/math/base/special/expm1",
"@stdlib/constants/float64/eps",
"@stdlib/math/base/special/exp"
]
Expand All @@ -73,6 +75,7 @@
"libpath": [],
"dependencies": [
"@stdlib/math/base/assert/is-nan",
"@stdlib/math/base/special/expm1",
"@stdlib/math/base/special/exp"
]
}
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3 changes: 2 additions & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/variance/src/main.c
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Expand Up @@ -19,6 +19,7 @@
#include "stdlib/stats/base/dists/lognormal/variance.h"
#include "stdlib/math/base/assert/is_nan.h"
#include "stdlib/math/base/special/exp.h"
#include "stdlib/math/base/special/expm1.h"

/**
* Returns the variance for a lognormal distribution with location `mu` and scale `sigma`.
Expand All @@ -41,5 +42,5 @@ double stdlib_base_dists_lognormal_variance( const double mu, const double sigma
return 0.0 / 0.0; // NaN
}
s2 = sigma * sigma;
return ( stdlib_base_exp( s2 ) - 1.0 ) * stdlib_base_exp( ( 2.0 * mu ) + s2 );
return stdlib_base_expm1( s2 ) * stdlib_base_exp( ( 2.0 * mu ) + s2 );
}
1 change: 0 additions & 1 deletion lib/node_modules/@stdlib/stats/base/dists/lognormal/variance/test/fixtures/julia/REQUIRE
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@@ -1,3 +1,2 @@
Distributions 0.23.8
julia 1.5
JSON 0.21
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