diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/lib/main.js index 423c9028090e..549ee1f519e0 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/lib/main.js @@ -21,7 +21,7 @@ // MODULES // 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 // @@ -29,6 +29,22 @@ var exp = require( '@stdlib/math/base/special/exp' ); /** * Returns the excess kurtosis for a lognormal distribution with location `mu` and scale `sigma`. * +* ## Method +* +* The excess kurtosis is +* +* ```tex +* e^{4\sigma^2} + 2e^{3\sigma^2} + 3e^{2\sigma^2} - 6 +* ``` +* +* which cancels for small \\(\sigma\\). With \\(u = e^{\sigma^2} - 1\\), evaluated by `expm1`, it expands to +* +* ```tex +* u(16 + u(15 + u(6 + u))) +* ``` +* +* whose terms are all positive. +* * @param {number} mu - location parameter * @param {PositiveNumber} sigma - scale parameter * @returns {number} excess kurtosis @@ -54,8 +70,7 @@ var exp = require( '@stdlib/math/base/special/exp' ); * // returns NaN */ function kurtosis( mu, sigma ) { - var out; - var s2; + var u; if ( isnan( mu ) || isnan( sigma ) || @@ -63,12 +78,8 @@ function kurtosis( mu, sigma ) { ) { return NaN; } - s2 = sigma * sigma; - out = exp( 4.0*s2 ); - out += 2.0 * exp( 3.0*s2 ); - out += 3.0 * exp( 2.0*s2 ); - out -= 6.0; - return out; + u = expm1( sigma*sigma ); + return u * ( 16.0 + ( u * ( 15.0 + ( u * ( 6.0 + u ) ) ) ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/manifest.json index c29ddd4f9b06..b1625c527f6a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/manifest.json @@ -40,7 +40,7 @@ "dependencies": [ "@stdlib/math/base/napi/binary", "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/exp" + "@stdlib/math/base/special/expm1" ] }, { @@ -56,7 +56,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/exp", + "@stdlib/math/base/special/expm1", "@stdlib/constants/float64/eps" ] }, @@ -73,7 +73,7 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/exp" + "@stdlib/math/base/special/expm1" ] } ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/src/main.c index 1091e649cf30..1ad4bd3237af 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/src/main.c @@ -18,11 +18,27 @@ #include "stdlib/stats/base/dists/lognormal/kurtosis.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 excess kurtosis for a lognormal distribution with location `mu` and scale `sigma`. * +* ## Method +* +* The excess kurtosis is +* +* ```tex +* e^{4\sigma^2} + 2e^{3\sigma^2} + 3e^{2\sigma^2} - 6 +* ``` +* +* which cancels for small \\(\sigma\\). With \\(u = e^{\sigma^2} - 1\\), evaluated by `expm1`, it expands to +* +* ```tex +* u(16 + u(15 + u(6 + u))) +* ``` +* +* whose terms are all positive. +* * @param mu location parameter * @param sigma scale parameter * @return excess kurtosis @@ -32,8 +48,7 @@ * // returns ~110.936 */ double stdlib_base_dists_lognormal_kurtosis( const double mu, const double sigma ) { - double out; - double s2; + double u; if ( stdlib_base_is_nan( mu ) || stdlib_base_is_nan( sigma ) || @@ -41,10 +56,6 @@ double stdlib_base_dists_lognormal_kurtosis( const double mu, const double sigma ) { return 0.0/0.0; // NaN } - s2 = sigma * sigma; - out = stdlib_base_exp( 4.0*s2 ); - out += 2.0 * stdlib_base_exp( 3.0*s2 ); - out += 3.0 * stdlib_base_exp( 2.0*s2 ); - out -= 6.0; - return out; + u = stdlib_base_expm1( sigma * sigma ); + return u * ( 16.0 + ( u * ( 15.0 + ( u * ( 6.0 + u ) ) ) ) ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/REQUIRE index 98be20b58ed3..308c3be89c85 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/REQUIRE @@ -1,3 +1,2 @@ -Distributions 0.23.8 julia 1.5 JSON 0.21 diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/data.json index f7e2042a57af..045e90418e55 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/data.json +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/data.json @@ -1 +1 @@ -{"sigma":[0.013606039203587494,1.6770196416730887,4.426416512870041,3.939767112070066,4.419662226502438,0.8434960457795337,1.0026940133952622,1.4512138282428566,2.8623145368917067,3.2153907122177996,2.549051222353713,0.7208063555120703,2.044091167217031,0.9107223308474277,0.32806114406364606,1.7706768795382821,2.7706240687282433,2.290652267933818,4.429448105152064,3.6411858326315416,3.936440891920885,2.6572952706035355,4.846500506506592,3.4914522517183633,4.514825261652415,3.3816883097647055,4.531386430969631,1.5646050466274741,1.1698142455987182,2.3306365033036047,0.25298270392462463,3.432215428336759,2.6393454298572716,4.546023064172649,4.9614981823819315,0.6767380270254053,1.995626862775618,0.9182724132017517,1.6123270518329025,1.176263648034963,4.161705200208267,3.8202396331483337,4.504624824960235,1.9047359026014143,0.03996494779838655,1.0943749037658457,4.294849529418365,1.7338675156060535,2.575391132109978,4.940118927276637,4.6043311839301815,4.766208202403544,0.223040099918973,2.8938559859622193,3.6441421854062006,3.774078854693675,2.281404509767518,1.8760172456551683,3.80300783924309,1.7744213999186365,2.480611887972033,0.9001588606748534,3.007506136357504,2.99031232372142,3.1316138424957716,3.626505161580307,1.7433973679516745,3.391897895536502,1.7749204524124174,4.153575862028073,1.908680439266962,4.6881269264290975,0.9231496485240065,3.5400867587100016,1.1607450221163806,4.806666723939346,2.683479522317742,3.6652189461301674,0.43170185675238004,1.5845150389696294,4.665099694101583,4.157859502858453,3.902770391049705,0.9327170836030874,2.168638486308275,4.997796469821671,3.5833264426009426,2.232959786563533,1.341290922694096,4.860616170905477,2.81668647327327,3.496961574934864,3.592712077690484,4.606904812578824,1.221039634545329,2.0474878204998936,4.775991769508673,3.2005905180987346,1.1102791583885163,4.517173024418933],"expected":[0.0029627772282978526,86904.32612102535,1.0884551812127136e34,9.205927173872686e26,8.570694117978124e33,40.57097462916551,113.02347398129417,5860.96113123167,1.7087123219377416e14,9.125455894930533e17,1.9449352569240494e11,19.975805678561414,1.8701350925232217e7,61.435473542836206,2.0207080750853397,305519.8480698636,2.1657186531854242e13,1.3173712422554023e9,1.211850959251774e34,1.0762506965795024e23,8.290046159529648e26,1.8507069543325483e12,6.365322628572092e40,1.501821208843442e21,2.570525418574072e35,7.346089523598491e19,4.680353750231139e35,21378.184211619016,400.03102625461463,2.753764569169632e9,1.1247575548773288,2.9116631204282466e20,1.2654699173055764e12,7.963149180311166e35,5.796666143283337e42,15.644800914707993,8.603750872707954e6,64.46248406783172,38219.60701320712,421.9616562892313,1.2233683097642807e30,2.2530773927674577e25,1.7790882302630783e35,2.1177298955578553e6,0.025613923280804585,219.97520809679804,1.1053996735304558e32,184640.86231706975,3.3359483533629706e11,2.485630020639736e42,6.728816398359076e36,2.904159117938304e39,0.8559062403015236,3.532055572328829e14,1.1730830263714398e23,5.543598714594206e24,1.1129010052559166e9,1.3802617072481334e6,1.3322219979787817e25,321799.3124232156,4.914289785487553e10,57.468152808846455,5.164623455702553e15,3.4190282136833995e15,1.0878296725197038e17,7.023703106411123e22,210107.91542297904,9.687038239190974e19,324036.5658544803,9.33529272228243e29,2.2472380548227155e6,1.5157385016621903e38,66.50824522254032,5.897787620089486e21,371.3336164258881,1.3672155967061007e40,3.237237724100069e12,2.1724715507692697e23,3.960706589227197,27171.320180376802,6.4043162912494e37,1.0764083038567397e30,2.8842213527928303e26,70.7403144211999,1.5060746781812477e8,2.4613727341799226e43,2.021918544042339e22,4.652789296591771e8,1879.5675199228124,1.1011657934479049e41,6.061768403997698e13,1.751870105915238e21,2.647069569361544e22,7.398109259386784e36,617.4468441893677,1.9761933212281045e7,4.218885118179443e39,6.241641662908753e17,248.55305197979465,2.7980710753276238e35],"mu":[-3.785188913233297,-2.3558649744770355,-3.3138459690143613,-2.9223611054467513,-2.277843450292301,-2.8313848475061523,-2.122842969889887,-2.779670277997986,-3.4129542144140266,-3.017605174232774,-3.2270755124211306,-3.4270122548111033,-3.9717943231511783,-2.3830370154185094,-2.5550404092066095,-2.8817967495314214,-2.502531286316559,-2.4357741219952023,-2.1733363701090442,-2.728269488988314,-2.710744423754661,-2.527014372496091,-3.6913646196420067,-3.9858664200566967,-3.3972121018385684,-2.6181944319390817,-2.737859280611349,-3.1187275564953567,-2.0777464142254476,-2.8035994714081585,-3.0331760887506274,-2.8664954691854305,-3.385305429742553,-2.3982491604332288,-3.4207936628141016,-2.7738508798259445,-3.3212546352727386,-3.133191803271066,-2.574504826434971,-2.003442385493707,-2.2254394340378583,-3.3018369649841675,-2.3637046976567095,-3.7428617372308106,-2.7093912186654125,-2.785996368097992,-2.0199160183078315,-3.632329689818935,-2.580119206736008,-3.930258571516214,-2.8283672729962146,-2.0052323273061843,-2.5568706518664057,-2.3781838978276753,-3.585998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diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/runner.jl index 0de76829cd1e..f51e34243b4a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/runner.jl @@ -16,7 +16,6 @@ # See the License for the specific language governing permissions and # limitations under the License. -import Distributions: kurtosis, LogNormal import JSON """ @@ -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 ] = kurtosis( LogNormal( mu[i], sigma[i] ) ); + # The excess kurtosis is evaluated in extended precision using the textbook formula `exp(4*sigma^2) + 2*exp(3*sigma^2) + 3*exp(2*sigma^2) - 6`, as subtracting `6` in double precision cancels for small `sigma`. + z = setprecision( BigFloat, 2048 ) do + s2 = BigFloat.( sigma ) .^ 2; + Float64.( exp.( 4 .* s2 ) .+ ( 2 .* exp.( 3 .* s2 ) ) .+ ( 3 .* exp.( 2 .* s2 ) ) .- 6 ); end # Store data to be written to file as a collection: @@ -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` (above `1e-154`, where `sigma^2` underflows): +mu = ( rand( 1000 ) .* 4.0 ) .- 2.0; +sigma = exp10.( range( -150.0, stop = -1.0, length = 1000 ) ); +gen( mu, sigma, "small_sigma.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/small_sigma.json b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/small_sigma.json new file mode 100644 index 000000000000..5af47be64d97 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/fixtures/julia/small_sigma.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.js index aee88f7fb4a0..1deb9467fedb 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.js +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.js @@ -22,16 +22,16 @@ var tape = require( 'tape' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); var kurtosis = require( './../lib' ); // FIXTURES // var data = require( './fixtures/julia/data.json' ); +var smallSigma = require( './fixtures/julia/small_sigma.json' ); // TESTS // @@ -76,9 +76,7 @@ tape( 'if provided a nonpositive `sigma`, the function returns `NaN`', function tape( 'the function returns the excess kurtosis of a lognormal distribution', function test( t ) { var expected; - var delta; var sigma; - var tol; var mu; var y; var i; @@ -89,13 +87,26 @@ tape( 'the function returns the excess kurtosis of a lognormal distribution', fu for ( i = 0; i < mu.length; i++ ) { y = kurtosis( mu[i], sigma[i] ); if ( expected[i] !== null ) { - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'mu:'+mu[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 10.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. mu: '+mu[i]+'. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 61 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function returns the excess kurtosis 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 = kurtosis( mu[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } } t.end(); diff --git a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.native.js index 305ee549209c..c38163adb777 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/lognormal/kurtosis/test/test.native.js @@ -24,15 +24,15 @@ var resolve = require( 'path' ).resolve; var tape = require( 'tape' ); var tryRequire = require( '@stdlib/utils/try-require' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var abs = require( '@stdlib/math/base/special/abs' ); +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); // FIXTURES // var data = require( './fixtures/julia/data.json' ); +var smallSigma = require( './fixtures/julia/small_sigma.json' ); // VARIABLES // @@ -88,9 +88,7 @@ tape( 'if provided a nonpositive `sigma`, the function returns `NaN`', opts, fun tape( 'the function returns the excess kurtosis of a lognormal distribution', opts, function test( t ) { var expected; - var delta; var sigma; - var tol; var mu; var y; var i; @@ -101,13 +99,26 @@ tape( 'the function returns the excess kurtosis of a lognormal distribution', op for ( i = 0; i < mu.length; i++ ) { y = kurtosis( mu[i], sigma[i] ); if ( expected[i] !== null ) { - if ( y === expected[i] ) { - t.strictEqual( y, expected[i], 'mu:'+mu[i]+', sigma: '+sigma[i]+', y: '+y+', expected: '+expected[i] ); - } else { - delta = abs( y - expected[ i ] ); - tol = 160.0 * EPS * abs( expected[ i ] ); - t.ok( delta <= tol, 'within tolerance. mu: '+mu[i]+'. sigma: '+sigma[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); - } + t.strictEqual( isAlmostSameValue( y, expected[ i ], 61 ), true, 'returns expected value' ); + } + } + t.end(); +}); + +tape( 'the function returns the excess kurtosis 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 = kurtosis( mu[i], sigma[i] ); + if ( expected[i] !== null ) { + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1 ), true, 'returns expected value' ); } } t.end();