<?php
namespace MathPHP\Tests\Probability\Distribution\Continuous;
use MathPHP\Exception;
use MathPHP\Probability\Distribution\Continuous\Beta;
class BetaTest extends \PHPUnit\Framework\TestCase
{
/**
* @test pdf
* @dataProvider dataProviderForPdf
* @param float $x
* @param float $α
* @param float $β
* @param float $expected_pdf
*/
public function testPdf(float $x, float $α, float $β, float $expected_pdf)
{
// Given
$beta = new Beta($α, $β);
// When
$pdf = $beta->pdf($x);
// Then
$this->assertEqualsWithDelta($expected_pdf, $pdf, 0.0000001);
}
/**
* @return array [x, α, β, pdf]
* Generated with http://keisan.casio.com/exec/system/1180573226
*/
public function dataProviderForPdf(): array
{
return [
[0, 1, 1, 1],
[0.01, 1, 1, 1],
[0.15, 1, 1, 1],
[0.81, 1, 1, 1],
[0.99, 1, 1, 1],
[1, 1, 1, 1],
[0, 2, 3, 0],
[0.01, 2, 3, 0.117612],
[0.02, 2, 3, 0.230496],
[0.03, 2, 3, 0.338724],
[0.04, 2, 3, 0.442368],
[0.05, 2, 3, 0.5415],
[0.06, 2, 3, 0.636192],
[0.07, 2, 3, 0.726516],
[0.08, 2, 3, 0.812544],
[0.09, 2, 3, 0.894348],
[0.1, 2, 3, 0.972],
[0.11, 2, 3, 1.045572],
[0.12, 2, 3, 1.115136],
[0.13, 2, 3, 1.180764],
[0.14, 2, 3, 1.242528],
[0.15, 2, 3, 1.3005],
[0.16, 2, 3, 1.354752],
[0.17, 2, 3, 1.405356],
[0.18, 2, 3, 1.452384],
[0.19, 2, 3, 1.495908],
[0.2, 2, 3, 1.536],
[0.21, 2, 3, 1.572732],
[0.22, 2, 3, 1.606176],
[0.23, 2, 3, 1.636404],
[0.24, 2, 3, 1.663488],
[0.25, 2, 3, 1.6875],
[0.26, 2, 3, 1.708512],
[0.27, 2, 3, 1.726596],
[0.28, 2, 3, 1.741824],
[0.29, 2, 3, 1.754268],
[0.3, 2, 3, 1.764],
[0.31, 2, 3, 1.771092],
[0.32, 2, 3, 1.775616],
[0.33, 2, 3, 1.777644],
[0.34, 2, 3, 1.777248],
[0.35, 2, 3, 1.7745],
[0.36, 2, 3, 1.769472],
[0.37, 2, 3, 1.762236],
[0.38, 2, 3, 1.752864],
[0.39, 2, 3, 1.741428],
[0.4, 2, 3, 1.728],
[0.41, 2, 3, 1.712652],
[0.42, 2, 3, 1.695456],
[0.43, 2, 3, 1.676484],
[0.44, 2, 3, 1.655808],
[0.45, 2, 3, 1.6335],
[0.46, 2, 3, 1.609632],
[0.47, 2, 3, 1.584276],
[0.48, 2, 3, 1.557504],
[0.49, 2, 3, 1.529388],
[0.5, 2, 3, 1.5],
[0.51, 2, 3, 1.469412],
[0.52, 2, 3, 1.437696],
[0.53, 2, 3, 1.404924],
[0.54, 2, 3, 1.371168],
[0.55, 2, 3, 1.3365],
[0.56, 2, 3, 1.300992],
[0.57, 2, 3, 1.264716],
[0.58, 2, 3, 1.227744],
[0.59, 2, 3, 1.190148],
[0.6, 2, 3, 1.152],
[0.61, 2, 3, 1.113372],
[0.62, 2, 3, 1.074336],
[0.63, 2, 3, 1.034964],
[0.64, 2, 3, 0.995328],
[0.65, 2, 3, 0.9555],
[0.66, 2, 3, 0.915552],
[0.67, 2, 3, 0.875556],
[0.68, 2, 3, 0.835584],
[0.69, 2, 3, 0.795708],
[0.7, 2, 3, 0.756],
[0.71, 2, 3, 0.716532],
[0.72, 2, 3, 0.677376],
[0.73, 2, 3, 0.638604],
[0.74, 2, 3, 0.600288],
[0.75, 2, 3, 0.5625],
[0.76, 2, 3, 0.525312],
[0.77, 2, 3, 0.488796],
[0.78, 2, 3, 0.453024],
[0.79, 2, 3, 0.418068],
[0.8, 2, 3, 0.384],
[0.81, 2, 3, 0.350892],
[0.82, 2, 3, 0.318816],
[0.83, 2, 3, 0.287844],
[0.84, 2, 3, 0.258048],
[0.85, 2, 3, 0.2295],
[0.86, 2, 3, 0.202272],
[0.87, 2, 3, 0.176436],
[0.88, 2, 3, 0.152064],
[0.89, 2, 3, 0.129228],
[0.9, 2, 3, 0.108],
[0.91, 2, 3, 0.088452],
[0.92, 2, 3, 0.070656],
[0.93, 2, 3, 0.054684],
[0.94, 2, 3, 0.040608],
[0.95, 2, 3, 0.0285],
[0.96, 2, 3, 0.018432],
[0.97, 2, 3, 0.010476],
[0.98, 2, 3, 0.004704],
[0.99, 2, 3, 0.001188],
[1, 2, 3, 0],
[0, 5.3, 4.1, 0],
[0.01, 5.3, 4.1, 8.992682837E-7],
[0.02, 5.3, 4.1, 1.716524432E-5],
[0.03, 5.3, 4.1, 9.506790967E-5],
[0.04, 5.3, 4.1, 3.17189614E-4],
[0.05, 5.3, 4.1, 8.01556921E-4],
[0.06, 5.3, 4.1, 0.0016988964],
[0.07, 5.3, 4.1, 0.003188885207],
[0.08, 5.3, 4.1, 0.005475822755],
[0.09, 5.3, 4.1, 0.008783978823],
[0.1, 5.3, 4.1, 0.01335278796],
[0.11, 5.3, 4.1, 0.01943201066],
[0.12, 5.3, 4.1, 0.02727695046],
[0.13, 5.3, 4.1, 0.03714379479],
[0.14, 5.3, 4.1, 0.04928513217],
[0.15, 5.3, 4.1, 0.06394568691],
[0.16, 5.3, 4.1, 0.08135830378],
[0.17, 5.3, 4.1, 0.1017402081],
[0.18, 5.3, 4.1, 0.125289561],
[0.19, 5.3, 4.1, 0.1521823254],
[0.2, 5.3, 4.1, 0.182569453],
[0.21, 5.3, 4.1, 0.2165744019],
[0.22, 5.3, 4.1, 0.254290988],
[0.23, 5.3, 4.1, 0.2957815744],
[0.24, 5.3, 4.1, 0.3410755976],
[0.25, 5.3, 4.1, 0.3901684309],
[0.26, 5.3, 4.1, 0.4430205794],
[0.27, 5.3, 4.1, 0.4995572033],
[0.28, 5.3, 4.1, 0.5596679626],
[0.29, 5.3, 4.1, 0.6232071758],
[0.3, 5.3, 4.1, 0.6899942834],
[0.31, 5.3, 4.1, 0.7598146065],
[0.32, 5.3, 4.1, 0.8324203897],
[0.33, 5.3, 4.1, 0.9075321165],
[0.34, 5.3, 4.1, 0.9848400846],
[0.35, 5.3, 4.1, 1.064006227],
[0.36, 5.3, 4.1, 1.144666166],
[0.37, 5.3, 4.1, 1.226431482],
[0.38, 5.3, 4.1, 1.30889219],
[0.39, 5.3, 4.1, 1.391619392],
[0.4, 5.3, 4.1, 1.474168111],
[0.41, 5.3, 4.1, 1.55608026],
[0.42, 5.3, 4.1, 1.636887763],
[0.43, 5.3, 4.1, 1.716115781],
[0.44, 5.3, 4.1, 1.793286033],
[0.45, 5.3, 4.1, 1.867920206],
[0.46, 5.3, 4.1, 1.939543413],
[0.47, 5.3, 4.1, 2.007687699],
[0.48, 5.3, 4.1, 2.071895558],
[0.49, 5.3, 4.1, 2.131723453],
[0.5, 5.3, 4.1, 2.186745318],
[0.51, 5.3, 4.1, 2.23655601],
[0.52, 5.3, 4.1, 2.2807747],
[0.53, 5.3, 4.1, 2.319048184],
[0.54, 5.3, 4.1, 2.351054078],
[0.55, 5.3, 4.1, 2.376503897],
[0.56, 5.3, 4.1, 2.395145972],
[0.57, 5.3, 4.1, 2.406768202],
[0.58, 5.3, 4.1, 2.411200616],
[0.59, 5.3, 4.1, 2.408317709],
[0.6, 5.3, 4.1, 2.398040553],
[0.61, 5.3, 4.1, 2.380338635],
[0.62, 5.3, 4.1, 2.355231427],
[0.63, 5.3, 4.1, 2.322789641],
[0.64, 5.3, 4.1, 2.283136168],
[0.65, 5.3, 4.1, 2.236446659],
[0.66, 5.3, 4.1, 2.182949752],
[0.67, 5.3, 4.1, 2.122926892],
[0.68, 5.3, 4.1, 2.056711757],
[0.69, 5.3, 4.1, 1.984689236],
[0.7, 5.3, 4.1, 1.907293967],
[0.71, 5.3, 4.1, 1.825008394],
[0.72, 5.3, 4.1, 1.73836034],
[0.73, 5.3, 4.1, 1.647920061],
[0.74, 5.3, 4.1, 1.554296779],
[0.75, 5.3, 4.1, 1.458134658],
[0.76, 5.3, 4.1, 1.360108233],
[0.77, 5.3, 4.1, 1.260917242],
[0.78, 5.3, 4.1, 1.16128088],
[0.79, 5.3, 4.1, 1.061931442],
[0.8, 5.3, 4.1, 0.96360735],
[0.81, 5.3, 4.1, 0.8670455576],
[0.82, 5.3, 4.1, 0.7729733206],
[0.83, 5.3, 4.1, 0.6820993361],
[0.84, 5.3, 4.1, 0.5951042469],
[0.85, 5.3, 4.1, 0.5126305178],
[0.86, 5.3, 4.1, 0.4352716926],
[0.87, 5.3, 4.1, 0.3635610522],
[0.88, 5.3, 4.1, 0.2979596986],
[0.89, 5.3, 4.1, 0.2388441045],
[0.9, 5.3, 4.1, 0.1864931841],
[0.91, 5.3, 4.1, 0.1410749612],
[0.92, 5.3, 4.1, 0.1026329449],
[0.93, 5.3, 4.1, 0.07107236645],
[0.94, 5.3, 4.1, 0.04614650559],
[0.95, 5.3, 4.1, 0.0274434489],
[0.96, 5.3, 4.1, 0.01437382816],
[0.97, 5.3, 4.1, 0.006160479551],
[0.98, 5.3, 4.1, 0.001831830498],
[0.99, 5.3, 4.1, 2.231780662E-4],
[1, 5.3, 4.1, 0],
[0, 3, 2, 0],
[0.01, 3, 2, 0.001188],
[0.15, 3, 2, 0.2295],
[0.81, 3, 2, 1.495908],
[0.99, 3, 2, 0.117612],
[1, 3, 2, 0],
[0, 10, 50, 0],
[0.01, 10, 50, 3.8395492E-7],
[0.15, 10, 50, 8.404355],
[0.81, 10, 50, 3.3949479E-26],
[0.99, 10, 50, 5.739479E-87],
[1, 10, 50, 0],
];
}
/**
* @test Constructor throws an Exception\OutOfBoundsException if alpha or beta is less than or equal to zero
* @dataProvider dataProviderForPdfAlphaBetaOutOfBoundsException
* @param float $α
* @param float $β
*/
public function testConstructorExceptionAlphaBetaLessThanEqualZero(float $α, float $β)
{
// Then
$this->expectException(Exception\OutOfBoundsException::class);
// When
new Beta($α, $β);
}
/**
* @return array [α, β]
*/
public function dataProviderForPdfAlphaBetaOutOfBoundsException(): array
{
return [
[1, -3],
[1, -2],
[1, -1],
[1, 0],
[-3, 1],
[-2, 1],
[-1, 1],
[0, 1],
];
}
/**
* @test pdf throws an Exception\OutOfBoundsException if the support x is less than 0 or greater than 1
* @dataProvider dataProviderForPdfSupportOutOfBoundsException
* @param float $x
*/
public function testPdfExceptionXOutOfBounds(float $x)
{
// Given
[$α, $β] = [1, 1];
$beta = new Beta($α, $β);
// Then
$this->expectException(Exception\OutOfBoundsException::class);
// When
$beta->pdf($x);
}
/**
* @return array
*/
public function dataProviderForPdfSupportOutOfBoundsException(): array
{
return [
[-3],
[-2],
[-1],
[-0.01],
[1.01],
[2],
[3],
];
}
/**
* @test cdf
* @dataProvider dataProviderForCdf
* @param float $x
* @param float $α
* @param float $β
* @param float $expected_cdf
*/
public function testCdf($x, $α, $β, $expected_cdf)
{
// Given
$beta = new Beta($α, $β);
// When
$cdf = $beta->cdf($x);
// Then
$this->assertEqualsWithDelta($expected_cdf, $cdf, 0.000001);
}
/**
* @return array [x, α, β, cdf]
* Generated with http://keisan.casio.com/exec/system/1180573226
*/
public function dataProviderForCdf()
{
return [
[0, 1, 1, 0],
[0.01, 1, 1, 0.01],
[0.02, 1, 1, 0.02],
[0.03, 1, 1, 0.03],
[0.04, 1, 1, 0.04],
[0.05, 1, 1, 0.05],
[0.06, 1, 1, 0.06],
[0.07, 1, 1, 0.07],
[0.08, 1, 1, 0.08],
[0.09, 1, 1, 0.09],
[0.1, 1, 1, 0.1],
[0.11, 1, 1, 0.11],
[0.12, 1, 1, 0.12],
[0.13, 1, 1, 0.13],
[0.14, 1, 1, 0.14],
[0.15, 1, 1, 0.15],
[0.16, 1, 1, 0.16],
[0.17, 1, 1, 0.17],
[0.18, 1, 1, 0.18],
[0.19, 1, 1, 0.19],
[0.2, 1, 1, 0.2],
[0.21, 1, 1, 0.21],
[0.22, 1, 1, 0.22],
[0.23, 1, 1, 0.23],
[0.24, 1, 1, 0.24],
[0.25, 1, 1, 0.25],
[0.26, 1, 1, 0.26],
[0.27, 1, 1, 0.27],
[0.28, 1, 1, 0.28],
[0.29, 1, 1, 0.29],
[0.3, 1, 1, 0.3],
[0.31, 1, 1, 0.31],
[0.32, 1, 1, 0.32],
[0.33, 1, 1, 0.33],
[0.34, 1, 1, 0.34],
[0.35, 1, 1, 0.35],
[0.36, 1, 1, 0.36],
[0.37, 1, 1, 0.37],
[0.38, 1, 1, 0.38],
[0.39, 1, 1, 0.39],
[0.4, 1, 1, 0.4],
[0.41, 1, 1, 0.41],
[0.42, 1, 1, 0.42],
[0.43, 1, 1, 0.43],
[0.44, 1, 1, 0.44],
[0.45, 1, 1, 0.45],
[0.46, 1, 1, 0.46],
[0.47, 1, 1, 0.47],
[0.48, 1, 1, 0.48],
[0.49, 1, 1, 0.49],
[0.5, 1, 1, 0.5],
[0.51, 1, 1, 0.51],
[0.52, 1, 1, 0.52],
[0.53, 1, 1, 0.53],
[0.54, 1, 1, 0.54],
[0.55, 1, 1, 0.55],
[0.56, 1, 1, 0.56],
[0.57, 1, 1, 0.57],
[0.58, 1, 1, 0.58],
[0.59, 1, 1, 0.59],
[0.6, 1, 1, 0.6],
[0.61, 1, 1, 0.61],
[0.62, 1, 1, 0.62],
[0.63, 1, 1, 0.63],
[0.64, 1, 1, 0.64],
[0.65, 1, 1, 0.65],
[0.66, 1, 1, 0.66],
[0.67, 1, 1, 0.67],
[0.68, 1, 1, 0.68],
[0.69, 1, 1, 0.69],
[0.7, 1, 1, 0.7],
[0.71, 1, 1, 0.71],
[0.72, 1, 1, 0.72],
[0.73, 1, 1, 0.73],
[0.74, 1, 1, 0.74],
[0.75, 1, 1, 0.75],
[0.76, 1, 1, 0.76],
[0.77, 1, 1, 0.77],
[0.78, 1, 1, 0.78],
[0.79, 1, 1, 0.79],
[0.8, 1, 1, 0.8],
[0.81, 1, 1, 0.81],
[0.82, 1, 1, 0.82],
[0.83, 1, 1, 0.83],
[0.84, 1, 1, 0.84],
[0.85, 1, 1, 0.85],
[0.86, 1, 1, 0.86],
[0.87, 1, 1, 0.87],
[0.88, 1, 1, 0.88],
[0.89, 1, 1, 0.89],
[0.9, 1, 1, 0.9],
[0.91, 1, 1, 0.91],
[0.92, 1, 1, 0.92],
[0.93, 1, 1, 0.93],
[0.94, 1, 1, 0.94],
[0.95, 1, 1, 0.95],
[0.96, 1, 1, 0.96],
[0.97, 1, 1, 0.97],
[0.98, 1, 1, 0.98],
[0.99, 1, 1, 0.99],
[1, 1, 1, 1],
[0, 2, 3, 0],
[0.01, 2, 3, 5.9203E-4],
[0.02, 2, 3, 0.00233648],
[0.03, 2, 3, 0.00518643],
[0.04, 2, 3, 0.00909568],
[0.05, 2, 3, 0.01401875],
[0.06, 2, 3, 0.01991088],
[0.07, 2, 3, 0.02672803],
[0.08, 2, 3, 0.03442688],
[0.09, 2, 3, 0.04296483],
[0.1, 2, 3, 0.0523],
[0.11, 2, 3, 0.06239123],
[0.12, 2, 3, 0.07319808],
[0.13, 2, 3, 0.08468083],
[0.14, 2, 3, 0.09680048],
[0.15, 2, 3, 0.10951875],
[0.16, 2, 3, 0.12279808],
[0.17, 2, 3, 0.13660163],
[0.18, 2, 3, 0.15089328],
[0.19, 2, 3, 0.16563763],
[0.2, 2, 3, 0.1808],
[0.21, 2, 3, 0.19634643],
[0.22, 2, 3, 0.21224368],
[0.23, 2, 3, 0.22845923],
[0.24, 2, 3, 0.24496128],
[0.25, 2, 3, 0.26171875],
[0.26, 2, 3, 0.27870128],
[0.27, 2, 3, 0.29587923],
[0.28, 2, 3, 0.31322368],
[0.29, 2, 3, 0.33070643],
[0.3, 2, 3, 0.3483],
[0.31, 2, 3, 0.36597763],
[0.32, 2, 3, 0.38371328],
[0.33, 2, 3, 0.40148163],
[0.34, 2, 3, 0.41925808],
[0.35, 2, 3, 0.43701875],
[0.36, 2, 3, 0.45474048],
[0.37, 2, 3, 0.47240083],
[0.38, 2, 3, 0.48997808],
[0.39, 2, 3, 0.50745123],
[0.4, 2, 3, 0.5248],
[0.41, 2, 3, 0.54200483],
[0.42, 2, 3, 0.55904688],
[0.43, 2, 3, 0.57590803],
[0.44, 2, 3, 0.59257088],
[0.45, 2, 3, 0.60901875],
[0.46, 2, 3, 0.62523568],
[0.47, 2, 3, 0.64120643],
[0.48, 2, 3, 0.65691648],
[0.49, 2, 3, 0.67235203],
[0.5, 2, 3, 0.6875],
[0.51, 2, 3, 0.70234803],
[0.52, 2, 3, 0.71688448],
[0.53, 2, 3, 0.73109843],
[0.54, 2, 3, 0.74497968],
[0.55, 2, 3, 0.75851875],
[0.56, 2, 3, 0.77170688],
[0.57, 2, 3, 0.78453603],
[0.58, 2, 3, 0.79699888],
[0.59, 2, 3, 0.80908883],
[0.6, 2, 3, 0.8208],
[0.61, 2, 3, 0.83212723],
[0.62, 2, 3, 0.84306608],
[0.63, 2, 3, 0.85361283],
[0.64, 2, 3, 0.86376448],
[0.65, 2, 3, 0.87351875],
[0.66, 2, 3, 0.88287408],
[0.67, 2, 3, 0.89182963],
[0.68, 2, 3, 0.90038528],
[0.69, 2, 3, 0.90854163],
[0.7, 2, 3, 0.9163],
[0.71, 2, 3, 0.92366243],
[0.72, 2, 3, 0.93063168],
[0.73, 2, 3, 0.93721123],
[0.74, 2, 3, 0.94340528],
[0.75, 2, 3, 0.94921875],
[0.76, 2, 3, 0.95465728],
[0.77, 2, 3, 0.95972723],
[0.78, 2, 3, 0.96443568],
[0.79, 2, 3, 0.96879043],
[0.8, 2, 3, 0.9728],
[0.81, 2, 3, 0.97647363],
[0.82, 2, 3, 0.97982128],
[0.83, 2, 3, 0.98285363],
[0.84, 2, 3, 0.98558208],
[0.85, 2, 3, 0.98801875],
[0.86, 2, 3, 0.99017648],
[0.87, 2, 3, 0.99206883],
[0.88, 2, 3, 0.99371008],
[0.89, 2, 3, 0.99511523],
[0.9, 2, 3, 0.9963],
[0.91, 2, 3, 0.99728083],
[0.92, 2, 3, 0.99807488],
[0.93, 2, 3, 0.99870003],
[0.94, 2, 3, 0.99917488],
[0.95, 2, 3, 0.99951875],
[0.96, 2, 3, 0.99975168],
[0.97, 2, 3, 0.99989443],
[0.98, 2, 3, 0.99996848],
[0.99, 2, 3, 0.99999603],
[1, 2, 3, 1],
[0, 3, 2, 0],
[0.01, 3, 2, 3.97E-6],
[0.02, 3, 2, 3.152E-5],
[0.03, 3, 2, 1.0557E-4],
[0.04, 3, 2, 2.4832E-4],
[0.05, 3, 2, 4.8125E-4],
[0.06, 3, 2, 8.2512E-4],
[0.07, 3, 2, 0.00129997],
[0.08, 3, 2, 0.00192512],
[0.09, 3, 2, 0.00271917],
[0.1, 3, 2, 0.0037],
[0.11, 3, 2, 0.00488477],
[0.12, 3, 2, 0.00628992],
[0.13, 3, 2, 0.00793117],
[0.14, 3, 2, 0.00982352],
[0.15, 3, 2, 0.01198125],
[0.16, 3, 2, 0.01441792],
[0.17, 3, 2, 0.01714637],
[0.18, 3, 2, 0.02017872],
[0.19, 3, 2, 0.02352637],
[0.2, 3, 2, 0.0272],
[0.21, 3, 2, 0.03120957],
[0.22, 3, 2, 0.03556432],
[0.23, 3, 2, 0.04027277],
[0.24, 3, 2, 0.04534272],
[0.25, 3, 2, 0.05078125],
[0.26, 3, 2, 0.05659472],
[0.27, 3, 2, 0.06278877],
[0.28, 3, 2, 0.06936832],
[0.29, 3, 2, 0.07633757],
[0.3, 3, 2, 0.0837],
[0.31, 3, 2, 0.09145837],
[0.32, 3, 2, 0.09961472],
[0.33, 3, 2, 0.10817037],
[0.34, 3, 2, 0.11712592],
[0.35, 3, 2, 0.12648125],
[0.36, 3, 2, 0.13623552],
[0.37, 3, 2, 0.14638717],
[0.38, 3, 2, 0.15693392],
[0.39, 3, 2, 0.16787277],
[0.4, 3, 2, 0.1792],
[0.41, 3, 2, 0.19091117],
[0.42, 3, 2, 0.20300112],
[0.43, 3, 2, 0.21546397],
[0.44, 3, 2, 0.22829312],
[0.45, 3, 2, 0.24148125],
[0.46, 3, 2, 0.25502032],
[0.47, 3, 2, 0.26890157],
[0.48, 3, 2, 0.28311552],
[0.49, 3, 2, 0.29765197],
[0.5, 3, 2, 0.3125],
[0.51, 3, 2, 0.32764797],
[0.52, 3, 2, 0.34308352],
[0.53, 3, 2, 0.35879357],
[0.54, 3, 2, 0.37476432],
[0.55, 3, 2, 0.39098125],
[0.56, 3, 2, 0.40742912],
[0.57, 3, 2, 0.42409197],
[0.58, 3, 2, 0.44095312],
[0.59, 3, 2, 0.45799517],
[0.6, 3, 2, 0.4752],
[0.61, 3, 2, 0.49254877],
[0.62, 3, 2, 0.51002192],
[0.63, 3, 2, 0.52759917],
[0.64, 3, 2, 0.54525952],
[0.65, 3, 2, 0.56298125],
[0.66, 3, 2, 0.58074192],
[0.67, 3, 2, 0.59851837],
[0.68, 3, 2, 0.61628672],
[0.69, 3, 2, 0.63402237],
[0.7, 3, 2, 0.6517],
[0.71, 3, 2, 0.66929357],
[0.72, 3, 2, 0.68677632],
[0.73, 3, 2, 0.70412077],
[0.74, 3, 2, 0.72129872],
[0.75, 3, 2, 0.73828125],
[0.76, 3, 2, 0.75503872],
[0.77, 3, 2, 0.77154077],
[0.78, 3, 2, 0.78775632],
[0.79, 3, 2, 0.80365357],
[0.8, 3, 2, 0.8192],
[0.81, 3, 2, 0.83436237],
[0.82, 3, 2, 0.84910672],
[0.83, 3, 2, 0.86339837],
[0.84, 3, 2, 0.87720192],
[0.85, 3, 2, 0.89048125],
[0.86, 3, 2, 0.90319952],
[0.87, 3, 2, 0.91531917],
[0.88, 3, 2, 0.92680192],
[0.89, 3, 2, 0.93760877],
[0.9, 3, 2, 0.9477],
[0.91, 3, 2, 0.95703517],
[0.92, 3, 2, 0.96557312],
[0.93, 3, 2, 0.97327197],
[0.94, 3, 2, 0.98008912],
[0.95, 3, 2, 0.98598125],
[0.96, 3, 2, 0.99090432],
[0.97, 3, 2, 0.99481357],
[0.98, 3, 2, 0.99766352],
[0.99, 3, 2, 0.99940797],
[1, 3, 2, 1],
[0, 10, 50, 0],
[0.01, 10, 50, 4.019555174E-10],
[0.02, 10, 50, 2.627230725E-7],
[0.03, 10, 50, 9.649195527E-6],
[0.04, 10, 50, 1.089160184E-4],
[0.05, 10, 50, 6.436109147E-4],
[0.06, 10, 50, 0.002524554335],
[0.07, 10, 50, 0.007461626373],
[0.08, 10, 50, 0.01792659751],
[0.09, 10, 50, 0.03676911366],
[0.1, 10, 50, 0.06658944558],
[0.11, 10, 50, 0.109084124],
[0.12, 10, 50, 0.1645800247],
[0.13, 10, 50, 0.2318848964],
[0.14, 10, 50, 0.3084655888],
[0.15, 10, 50, 0.3908704946],
[0.16, 10, 50, 0.4752657543],
[0.17, 10, 50, 0.5579559892],
[0.18, 10, 50, 0.6357944535],
[0.19, 10, 50, 0.7064347707],
[0.2, 10, 50, 0.7684204704],
[0.21, 10, 50, 0.8211398301],
[0.22, 10, 50, 0.8646892754],
[0.23, 10, 50, 0.8996908182],
[0.24, 10, 50, 0.9271020689],
[0.25, 10, 50, 0.9480459701],
[0.26, 10, 50, 0.9636753835],
[0.27, 10, 50, 0.9750774712],
[0.28, 10, 50, 0.9832155754],
[0.29, 10, 50, 0.9889021129],
[0.3, 10, 50, 0.9927943681],
[0.31, 10, 50, 0.9954052423],
[0.32, 10, 50, 0.9971222339],
[0.33, 10, 50, 0.9982295758],
[0.34, 10, 50, 0.9989301123],
[0.35, 10, 50, 0.9993649151],
[0.36, 10, 50, 0.9996297151],
[0.37, 10, 50, 0.9997879625],
[0.38, 10, 50, 0.9998807638],
[0.39, 10, 50, 0.9999341655],
[0.4, 10, 50, 0.9999643168],
[0.41, 10, 50, 0.9999810182],
[0.42, 10, 50, 0.9999900926],
[0.43, 10, 50, 0.9999949278],
[0.44, 10, 50, 0.9999974537],
[0.45, 10, 50, 0.9999987471],
[0.46, 10, 50, 0.999999396],
[0.47, 10, 50, 0.9999997149],
[0.48, 10, 50, 0.9999998682],
[0.49, 10, 50, 0.9999999404],
[0.5, 10, 50, 0.9999999737],
[0.51, 10, 50, 0.9999999886],
[0.52, 10, 50, 0.9999999952],
[0.53, 10, 50, 0.999999998],
[0.54, 10, 50, 0.9999999992],
[0.55, 10, 50, 0.9999999997],
[0.56, 10, 50, 0.9999999999],
[0.57, 10, 50, 1],
[0.58, 10, 50, 1],
[0.59, 10, 50, 1],
[0.6, 10, 50, 1],
[0.61, 10, 50, 1],
[0.62, 10, 50, 1],
[0.63, 10, 50, 1],
[0.64, 10, 50, 1],
[0.65, 10, 50, 1],
[0.66, 10, 50, 1],
[0.67, 10, 50, 1],
[0.68, 10, 50, 1],
[0.69, 10, 50, 1],
[0.7, 10, 50, 1],
[0.71, 10, 50, 1],
[0.72, 10, 50, 1],
[0.73, 10, 50, 1],
[0.74, 10, 50, 1],
[0.75, 10, 50, 1],
[0.76, 10, 50, 1],
[0.77, 10, 50, 1],
[0.78, 10, 50, 1],
[0.79, 10, 50, 1],
[0.8, 10, 50, 1],
[0.81, 10, 50, 1],
[0.82, 10, 50, 1],
[0.83, 10, 50, 1],
[0.84, 10, 50, 1],
[0.85, 10, 50, 1],
[0.86, 10, 50, 1],
[0.87, 10, 50, 1],
[0.88, 10, 50, 1],
[0.89, 10, 50, 1],
[0.9, 10, 50, 1],
[0.91, 10, 50, 1],
[0.92, 10, 50, 1],
[0.93, 10, 50, 1],
[0.94, 10, 50, 1],
[0.95, 10, 50, 1],
[0.96, 10, 50, 1],
[0.97, 10, 50, 1],
[0.98, 10, 50, 1],
[0.99, 10, 50, 1],
[1, 10, 50, 1],
];
}
/**
* @test mean
* @dataProvider dataProviderForMean
* @param float $α
* @param float $β
* @param float $μ
*/
public function testMean(float $α, float $β, float $μ)
{
// Given
$beta = new Beta($α, $β);
// When
$mean = $beta->mean();
// Then
$this->assertEqualsWithDelta($μ, $mean, 0.000001);
}
/**
* @return array [α, β, μ]
*/
public function dataProviderForMean(): array
{
return [
[1, 1, 0.5],
[1, 2, 0.33333333],
[2, 1, 0.66666666],
];
}
/**
* @test median
* @dataProvider dataProviderForMedian
* @param float $α
* @param float $β
* @param float $expected
*/
public function testMedian(float $α, float $β, float $expected)
{
// Given
$beta = new Beta($α, $β);
// When
$median = $beta->median();
// Then
$this->assertEqualsWithDelta($expected, $median, 0.000001);
}
/**
* Data generated with calculator: https://captaincalculator.com/math/statistics/beta-distribution-calculator/
* @return array [α, β, μ]
*/
public function dataProviderForMedian(): array
{
return [
// α == β
[1, 1, 0.5],
[2, 2, 0.5],
[3, 3, 0.5],
// α == 1, β > 0
[1, 0.1, 0.99902344],
[1, 0.5, 0.75],
[1, 2, 0.29289322],
[1, 3, 0.20629947],
[1, 4, 0.15910358],
[1, 5, 0.12944944],
// β == 1, α > 0
[0.1, 1, 0.00097656],
[0.5, 1, 0.25],
[2, 1, 0.70710678],
[3, 1, 0.79370053],
[4, 1, 0.84089642],
[5, 1, 0.87055056],
// α == 3, β == 2
[3, 2, 0.61427243],
// α == 2, β == 3
[2, 3, 0.38572757],
];
}
/**
* @test median when it is approximated
* @dataProvider dataProviderForMedianApproximation
* @param float $α
* @param float $β
* @param float $expected
* @param float $expectedError
*/
public function testMedianApproximation(float $α, float $β, float $expected, float $expectedError)
{
// Given
$beta = new Beta($α, $β);
// When
$median = $beta->median();
// Then
$ε = \abs($expected - $median);
$η = $ε / $expected;
$this->assertLessThan($expectedError, $η);
}
/**
* Data generated with calculator: https://captaincalculator.com/math/statistics/beta-distribution-calculator/
* @return array [α, β, μ]
*/
public function dataProviderForMedianApproximation(): array
{
return [
// α ≥ 2 and β ≥ 2 the error it is less than 1%
[2, 4, 0.31381017, 0.01],
[4, 2, 0.68618983, 0.01],
[4, 5, 0.4401552, 0.01],
[7, 4, 0.64490003, 0.01],
// α, β ≥ 1 the error is less than 4%
[1.8, 1.1, 0.6513904, 0.04],
[1.4, 1.3, 0.52366548, 0.04],
];
}
/**
* @test mode
* @dataProvider dataProviderForMode
* @param float $α
* @param float $β
* @param float $expected
*/
public function testMode(float $α, float $β, float $expected)
{
// Given
$beta = new Beta($α, $β);
// When
$mode = $beta->mode();
// Then
$this->assertEqualsWithDelta($expected, $mode, 0.000001);
}
/**
* Data generated with calculator: https://captaincalculator.com/math/statistics/beta-distribution-calculator/
* @return array [α, β, μ]
*/
public function dataProviderForMode(): array
{
return [
[1, 2, 0],
[1, 3, 0],
[2, 1, 1],
[3, 1, 1],
[2, 2, 0.5],
[4, 5, 0.42857143],
[7, 4, 0.66666667],
];
}
/**
* @test variance
* @dataProvider dataProviderForVariance
* @param float $α
* @param float $β
* @param float $expected
*/
public function testVariance(float $α, float $β, float $expected)
{
// Given
$beta = new Beta($α, $β);
// When
$variance = $beta->variance();
// Then
$this->assertEqualsWithDelta($expected, $variance, 0.000001);
}
/**
* Data generated with calculator: https://captaincalculator.com/math/statistics/beta-distribution-calculator/
* @return array [α, β, var]
*/
public function dataProviderForVariance(): array
{
return [
[1, 2, 0.05555556],
[1, 3, 0.0375],
[2, 1, 0.05555556],
[3, 1, 0.0375],
[2, 2, 0.05],
[4, 5, 0.02469136],
[7, 4, 0.01928375],
];
}
/**
* @test inverse
* @dataProvider dataProviderForInverse
* @param float $α
* @param float $β
* @param float $x
* @param float $expected_inverse
* @throws \Exception
*/
public function testInverse(float $α, float $β, float $x, float $expected_inverse)
{
// Given
$beta = new Beta($α, $β);
// When
$inverse = $beta->inverse($x);
// Then
$this->assertEqualsWithDelta($expected_inverse, $inverse, 0.0000001);
}
/**
* @return array [α, β, x, inverse]
* Generated with R (stats) qbeta(x, α, β)
*/
public function dataProviderForInverse(): array
{
return [
[1, 1, 0, 0],
[1, 1, 0.01, 0.01],
[1, 1, 0.1, 0.1],
[1, 1, 0.2, 0.2],
[1, 1, 0.3, 0.3],
[1, 1, 0.4, 0.4],
[1, 1, 0.5, 0.5],
[1, 1, 0.6, 0.6],
[1, 1, 0.7, 0.7],
[1, 1, 0.8, 0.8],
[1, 1, 0.9, 0.9],
[1, 1, 0.99, 0.99],
[1, 1, 1, 1],
[2, 1, 0, 0],
[2, 1, 0.01, 0.1],
[2, 1, 0.1, 0.3162278],
[2, 1, 0.2, 0.4472136],
[2, 1, 0.3, 0.5477226],
[2, 1, 0.4, 0.6324555],
[2, 1, 0.5, 0.7071068],
[2, 1, 0.6, 0.7745967],
[2, 1, 0.7, 0.83666],
[2, 1, 0.8, 0.8944272],
[2, 1, 0.9, 0.9486833],
[2, 1, 0.99, 0.9949874],
[2, 1, 1, 1],
[1, 2, 0, 0],
[1, 2, 0.01, 0.005012563],
[1, 2, 0.1, 0.0513167],
[1, 2, 0.2, 0.1055728],
[1, 2, 0.3, 0.16334],
[1, 2, 0.4, 0.2254033],
[1, 2, 0.5, 0.2928932],
[1, 2, 0.6, 0.3675445],
[1, 2, 0.7, 0.4522774],
[1, 2, 0.8, 0.5527864],
[1, 2, 0.9, 0.6837722],
[1, 2, 0.99, 0.9],
[1, 2, 1, 1],
[2, 3, 0, 0],
[2, 3, 0.01, 0.04199864],
[2, 3, 0.1, 0.1425593],
[2, 3, 0.2, 0.2123171],
[2, 3, 0.3, 0.2723839],
[2, 3, 0.4, 0.3291665],
[2, 3, 0.5, 0.3857276],
[2, 3, 0.6, 0.4445],
[2, 3, 0.7, 0.5084048],
[2, 3, 0.8, 0.5824536],
[2, 3, 0.9, 0.6795394],
[2, 3, 0.99, 0.8591325],
[2, 3, 1, 1],
[4, 5, 0.2, 0.3032258],
[10, 5, 0.01, 0.3725653],
[10, 5, 0.5, 0.6742488],
[10, 5, 0.99, 0.8980714],
];
}
/**
* @test inverse throws an exception if it fails to converge on a guess within the tolerance
* @throws Exception\MathException
*/
public function testInverseFailToConvergeException()
{
// Given
[$α, $β, $x] = [2, 5, 0.6];
$tolerance = 1.0e-15;
$max_iterations = 2;
$beta = new Beta($α, $β);
// Then
$this->expectException(Exception\MathException::class);
// When
$inverse = $beta->inverse($x, $tolerance, $max_iterations);
}
/**
* @test rand
*/
public function testRand()
{
foreach (\range(1, 10) as $α) {
foreach (\range(1, 10) as $β) {
// Given
$beta = new Beta($α, $β);
foreach (\range(1, 3) as $_) {
// When
$random = $beta->rand();
// Then
$this->assertTrue(\is_numeric($random));
}
}
}
}
}