diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/lib/main.js index 90b64b7f4322..2c26bc9f96dc 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/lib/main.js @@ -21,7 +21,9 @@ // MODULES // var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var expm1 = require( '@stdlib/math/base/special/expm1' ); var pow = require( '@stdlib/math/base/special/pow' ); +var LN2 = require( '@stdlib/constants/float64/ln-two' ); // MAIN // @@ -70,7 +72,8 @@ function median( a, b ) { ) { return NaN; } - return pow( 1.0 - pow( 2.0, -1.0/b ), 1.0/a ); + // `1 - 2^(-1/b)` cancels for large `b`; `-expm1(-ln(2)/b)` is the same value without the subtraction: + return pow( -expm1( -LN2/b ), 1.0/a ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/manifest.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/manifest.json index 330f7bc78ef1..427481ad1273 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/manifest.json +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/manifest.json @@ -40,7 +40,9 @@ "dependencies": [ "@stdlib/math/base/napi/binary", "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/pow" + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/pow", + "@stdlib/constants/float64/ln-two" ] }, { @@ -56,7 +58,9 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/assert/is-nan", + "@stdlib/math/base/special/expm1", "@stdlib/math/base/special/pow", + "@stdlib/constants/float64/ln-two", "@stdlib/constants/float64/eps" ] }, @@ -73,7 +77,9 @@ "libpath": [], "dependencies": [ "@stdlib/math/base/assert/is-nan", - "@stdlib/math/base/special/pow" + "@stdlib/math/base/special/expm1", + "@stdlib/math/base/special/pow", + "@stdlib/constants/float64/ln-two" ] } ] diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/src/main.c index 13964db45d21..f03ad2cd99a1 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/src/main.c @@ -18,7 +18,9 @@ #include "stdlib/stats/base/dists/kumaraswamy/median.h" #include "stdlib/math/base/assert/is_nan.h" +#include "stdlib/math/base/special/expm1.h" #include "stdlib/math/base/special/pow.h" +#include "stdlib/constants/float64/ln_two.h" /** * Returns the median of a Kumaraswamy's double bounded distribution. @@ -39,5 +41,6 @@ double stdlib_base_dists_kumaraswamy_median( const double a, const double b ) { ) { return 0.0/0.0; // NaN } - return stdlib_base_pow( 1.0 - stdlib_base_pow( 2.0, -1.0/b ), 1.0/a ); + // `1 - 2^(-1/b)` cancels for large `b`; `-expm1(-ln(2)/b)` is the same value without the subtraction: + return stdlib_base_pow( -stdlib_base_expm1( -STDLIB_CONSTANT_FLOAT64_LN2 / b ), 1.0/a ); } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/REQUIRE index 98be20b58ed3..308c3be89c85 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/REQUIRE +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/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/kumaraswamy/median/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/data.json index 0f6cab2b3bc4..81daeea066e7 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/data.json +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/data.json @@ -1 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/large_b.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/large_b.json new file mode 100644 index 000000000000..aa851007171c --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/large_b.json @@ -0,0 +1 @@ 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diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/runner.jl index 2ba0edb566ea..1bc4efb9460c 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/fixtures/julia/runner.jl +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/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: median, Kumaraswamy import JSON """ @@ -24,6 +23,8 @@ import JSON Generate fixture data and write to file. +The median is evaluated in extended precision from the textbook formula `(1 - 2^(-1/b))^(1/a)`, as forming `1 - 2^(-1/b)` in double precision cancels for large `b`. + # Arguments * `a`: first shape parameter @@ -39,9 +40,8 @@ julia> gen( a, b, \"data.json\" ); ``` """ function gen( a, b, name ) - z = Array{Float64}( undef, length(a) ); - for i in eachindex(a) - z[ i ] = median( Kumaraswamy( a[ i ], b[ i ] ) ); + z = setprecision( BigFloat, 2048 ) do + Float64.( ( 1 .- BigFloat( 2 ) .^ ( -1 ./ BigFloat.( b ) ) ) .^ ( 1 ./ BigFloat.( a ) ) ) end # Store data to be written to file as a collection: @@ -71,3 +71,8 @@ dir = dirname( file ); a = rand( 1000 ); b = rand( 1000 ); gen( a, b, "data.json" ); + +# Large `b`: +a = ( rand( 1000 ) .* 5.0 ) .+ 0.5; +b = exp10.( range( 0.0, stop = 15.0, length = 1000 ) ); +gen( a, b, "large_b.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.js index e01085becdc1..8f5da9324ce9 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.js @@ -31,6 +31,7 @@ var median = require( './../lib' ); // FIXTURES // var data = require( './fixtures/julia/data.json' ); +var largeB = require( './fixtures/julia/large_b.json' ); // TESTS // @@ -114,7 +115,24 @@ tape( 'the function returns the median of a Kumaraswamy distribution', function b = data.b; for ( i = 0; i < expected.length; i++ ) { y = median( a[i], b[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 9 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 442 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns the median of a Kumaraswamy distribution with a large `b`', function test( t ) { + var expected; + var a; + var b; + var i; + var y; + + expected = largeB.expected; + a = largeB.a; + b = largeB.b; + for ( i = 0; i < expected.length; i++ ) { + y = median( a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 24 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.native.js index e62d34617579..9307b5903e04 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/median/test/test.native.js @@ -32,6 +32,7 @@ var NINF = require( '@stdlib/constants/float64/ninf' ); // FIXTURES // var data = require( './fixtures/julia/data.json' ); +var largeB = require( './fixtures/julia/large_b.json' ); // VARIABLES // @@ -126,7 +127,24 @@ tape( 'the function returns the median of a Kumaraswamy distribution', opts, fun b = data.b; for ( i = 0; i < expected.length; i++ ) { y = median( a[i], b[i] ); - t.strictEqual( isAlmostSameValue( y, expected[ i ], 9 ), true, 'returns expected value' ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 442 ), true, 'returns expected value' ); + } + t.end(); +}); + +tape( 'the function returns the median of a Kumaraswamy distribution with a large `b`', opts, function test( t ) { + var expected; + var a; + var b; + var i; + var y; + + expected = largeB.expected; + a = largeB.a; + b = largeB.b; + for ( i = 0; i < expected.length; i++ ) { + y = median( a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 24 ), true, 'returns expected value' ); } t.end(); });