1 /* 2 * Copyright (C) 2012, 2013 Apple Inc. All rights reserved. 3 * 4 * Redistribution and use in source and binary forms, with or without 5 * modification, are permitted provided that the following conditions 6 * are met: 7 * 1. Redistributions of source code must retain the above copyright 8 * notice, this list of conditions and the following disclaimer. 9 * 2. Redistributions in binary form must reproduce the above copyright 10 * notice, this list of conditions and the following disclaimer in the 11 * documentation and/or other materials provided with the distribution. 12 * 13 * THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS'' 14 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, 15 * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS 17 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 18 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 19 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 20 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 21 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 22 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF 23 * THE POSSIBILITY OF SUCH DAMAGE. 24 */ 25 26 var Statistics = new (function () { 27 28 this.max = function (values) { 29 return Math.max.apply(Math, values); 30 } 31 32 this.min = function (values) { 33 return Math.min.apply(Math, values); 34 } 35 36 this.sum = function (values) { 37 return values.reduce(function (a, b) { return a + b; }, 0); 38 } 39 40 this.squareSum = function (values) { 41 return values.reduce(function (sum, value) { return sum + value * value;}, 0); 42 } 43 44 // With sum and sum of squares, we can compute the sample standard deviation in O(1). 45 // See https://rniwa.com/2012-11-10/sample-standard-deviation-in-terms-of-sum-and-square-sum-of-samples/ 46 this.sampleStandardDeviation = function (numberOfSamples, sum, squareSum) { 47 if (numberOfSamples < 2) 48 return 0; 49 return Math.sqrt(squareSum / (numberOfSamples - 1) 50 - sum * sum / (numberOfSamples - 1) / numberOfSamples); 51 } 52 53 this.supportedConfidenceLevels = function () { 54 var supportedLevels = []; 55 for (var quantile in tDistributionInverseCDF) 56 supportedLevels.push((1 - (1 - quantile) * 2).toFixed(2)); 57 return supportedLevels; 58 } 59 60 // Computes the delta d s.t. (mean - d, mean + d) is the confidence interval with the specified confidence level in O(1). 61 this.confidenceIntervalDelta = function (confidenceLevel, numberOfSamples, sum, squareSum) { 62 var probability = (1 - (1 - confidenceLevel) / 2); 63 if (!(probability in tDistributionInverseCDF)) { 64 console.warn('We only support ' + this.supportedConfidenceLevels().map( 65 function (level) { return level * 100 + '%'; } ).join(', ') + ' confidence intervals.'); 66 return NaN; 67 } 68 if (numberOfSamples < 2) 69 return Number.POSITIVE_INFINITY; 70 71 var cdfForProbability = tDistributionInverseCDF[probability]; 72 var degreesOfFreedom = numberOfSamples - 1; 73 74 // tDistributionQuantile(degreesOfFreedom, confidenceLevel) * sampleStandardDeviation / sqrt(numberOfSamples) * S/sqrt(numberOfSamples) 75 if (degreesOfFreedom <= 100) 76 var quantile = cdfForProbability[degreesOfFreedom - 1]; // The first entry is for the one degree of freedom. 77 else if (degreesOfFreedom <= 300) 78 var quantile = cdfForProbability[Math.round(degreesOfFreedom / 10) + 100 - 10 - 1]; 79 else if (degreesOfFreedom <= 1300) 80 var quantile = cdfForProbability[Math.round(degreesOfFreedom / 100) + 120 - 3 - 1]; 81 else 82 var quantile = cdfForProbability[cdfForProbability.length - 1]; 83 return quantile * this.sampleStandardDeviation(numberOfSamples, sum, squareSum) / Math.sqrt(numberOfSamples); 84 } 85 86 this.confidenceInterval = function (values, probability) { 87 var sum = this.sum(values); 88 var mean = sum / values.length; 89 var delta = this.confidenceIntervalDelta(probability || 0.95, values.length, sum, this.squareSum(values)); 90 return [mean - delta, mean + delta]; 91 } 92 93 // See http://en.wikipedia.org/wiki/Student's_t-distribution#Table_of_selected_values 94 // This table contains one sided (a.k.a. tail) values. 95 // Use TINV((1 - probability) * 2, df) in your favorite spreadsheet software to compute these. 96 // The spacing of the values with df greater than 100 maintains error less than 0.8%. 97 var tDistributionInverseCDF = { 98 0.9: [ 99 // 1 - 100 step 1 100 3.077684, 1.885618, 1.637744, 1.533206, 1.475884, 1.439756, 1.414924, 1.396815, 1.383029, 1.372184, 101 1.363430, 1.356217, 1.350171, 1.345030, 1.340606, 1.336757, 1.333379, 1.330391, 1.327728, 1.325341, 102 1.323188, 1.321237, 1.319460, 1.317836, 1.316345, 1.314972, 1.313703, 1.312527, 1.311434, 1.310415, 103 1.309464, 1.308573, 1.307737, 1.306952, 1.306212, 1.305514, 1.304854, 1.304230, 1.303639, 1.303077, 104 1.302543, 1.302035, 1.301552, 1.301090, 1.300649, 1.300228, 1.299825, 1.299439, 1.299069, 1.298714, 105 1.298373, 1.298045, 1.297730, 1.297426, 1.297134, 1.296853, 1.296581, 1.296319, 1.296066, 1.295821, 106 1.295585, 1.295356, 1.295134, 1.294920, 1.294712, 1.294511, 1.294315, 1.294126, 1.293942, 1.293763, 107 1.293589, 1.293421, 1.293256, 1.293097, 1.292941, 1.292790, 1.292643, 1.292500, 1.292360, 1.292224, 108 1.292091, 1.291961, 1.291835, 1.291711, 1.291591, 1.291473, 1.291358, 1.291246, 1.291136, 1.291029, 109 1.290924, 1.290821, 1.290721, 1.290623, 1.290527, 1.290432, 1.290340, 1.290250, 1.290161, 1.290075, 110 // 110 - 300 step 10 111 1.289295, 1.288646, 1.288098, 1.287628, 1.287221, 1.286865, 1.286551, 1.286272, 1.286023, 1.285799, 112 1.285596, 1.285411, 1.285243, 1.285089, 1.284947, 1.284816, 1.284695, 1.284582, 1.284478, 1.284380, 113 // 400 - 1300 step 100 114 1.283672, 1.283247, 1.282964, 1.282762, 1.282611, 1.282493, 1.282399, 1.282322, 1.282257, 1.282203, 115 // Infinity 116 1.281548], 117 0.95: [ 118 // 1 - 100 step 1 119 6.313752, 2.919986, 2.353363, 2.131847, 2.015048, 1.943180, 1.894579, 1.859548, 1.833113, 1.812461, 120 1.795885, 1.782288, 1.770933, 1.761310, 1.753050, 1.745884, 1.739607, 1.734064, 1.729133, 1.724718, 121 1.720743, 1.717144, 1.713872, 1.710882, 1.708141, 1.705618, 1.703288, 1.701131, 1.699127, 1.697261, 122 1.695519, 1.693889, 1.692360, 1.690924, 1.689572, 1.688298, 1.687094, 1.685954, 1.684875, 1.683851, 123 1.682878, 1.681952, 1.681071, 1.680230, 1.679427, 1.678660, 1.677927, 1.677224, 1.676551, 1.675905, 124 1.675285, 1.674689, 1.674116, 1.673565, 1.673034, 1.672522, 1.672029, 1.671553, 1.671093, 1.670649, 125 1.670219, 1.669804, 1.669402, 1.669013, 1.668636, 1.668271, 1.667916, 1.667572, 1.667239, 1.666914, 126 1.666600, 1.666294, 1.665996, 1.665707, 1.665425, 1.665151, 1.664885, 1.664625, 1.664371, 1.664125, 127 1.663884, 1.663649, 1.663420, 1.663197, 1.662978, 1.662765, 1.662557, 1.662354, 1.662155, 1.661961, 128 1.661771, 1.661585, 1.661404, 1.661226, 1.661052, 1.660881, 1.660715, 1.660551, 1.660391, 1.660234, 129 // 110 - 300 step 10 130 1.658824, 1.657651, 1.656659, 1.655811, 1.655076, 1.654433, 1.653866, 1.653363, 1.652913, 1.652508, 131 1.652142, 1.651809, 1.651506, 1.651227, 1.650971, 1.650735, 1.650517, 1.650314, 1.650125, 1.649949, 132 // 400 - 1300 step 100 133 1.648672, 1.647907, 1.647397, 1.647033, 1.646761, 1.646548, 1.646379, 1.646240, 1.646124, 1.646027, 134 // Infinity 135 1.644847], 136 0.975: [ 137 // 1 - 100 step 1 138 12.706205, 4.302653, 3.182446, 2.776445, 2.570582, 2.446912, 2.364624, 2.306004, 2.262157, 2.228139, 139 2.200985, 2.178813, 2.160369, 2.144787, 2.131450, 2.119905, 2.109816, 2.100922, 2.093024, 2.085963, 140 2.079614, 2.073873, 2.068658, 2.063899, 2.059539, 2.055529, 2.051831, 2.048407, 2.045230, 2.042272, 141 2.039513, 2.036933, 2.034515, 2.032245, 2.030108, 2.028094, 2.026192, 2.024394, 2.022691, 2.021075, 142 2.019541, 2.018082, 2.016692, 2.015368, 2.014103, 2.012896, 2.011741, 2.010635, 2.009575, 2.008559, 143 2.007584, 2.006647, 2.005746, 2.004879, 2.004045, 2.003241, 2.002465, 2.001717, 2.000995, 2.000298, 144 1.999624, 1.998972, 1.998341, 1.997730, 1.997138, 1.996564, 1.996008, 1.995469, 1.994945, 1.994437, 145 1.993943, 1.993464, 1.992997, 1.992543, 1.992102, 1.991673, 1.991254, 1.990847, 1.990450, 1.990063, 146 1.989686, 1.989319, 1.988960, 1.988610, 1.988268, 1.987934, 1.987608, 1.987290, 1.986979, 1.986675, 147 1.986377, 1.986086, 1.985802, 1.985523, 1.985251, 1.984984, 1.984723, 1.984467, 1.984217, 1.983972, 148 // 110 - 300 step 10 149 1.981765, 1.979930, 1.978380, 1.977054, 1.975905, 1.974902, 1.974017, 1.973231, 1.972528, 1.971896, 150 1.971325, 1.970806, 1.970332, 1.969898, 1.969498, 1.969130, 1.968789, 1.968472, 1.968178, 1.967903, 151 // 400 - 1300 step 100 152 1.965912, 1.964720, 1.963926, 1.963359, 1.962934, 1.962603, 1.962339, 1.962123, 1.961943, 1.961790, 153 // Infinity 154 1.959964], 155 0.99: [ 156 // 1 - 100 step 1 157 31.820516, 6.964557, 4.540703, 3.746947, 3.364930, 3.142668, 2.997952, 2.896459, 2.821438, 2.763769, 158 2.718079, 2.680998, 2.650309, 2.624494, 2.602480, 2.583487, 2.566934, 2.552380, 2.539483, 2.527977, 159 2.517648, 2.508325, 2.499867, 2.492159, 2.485107, 2.478630, 2.472660, 2.467140, 2.462021, 2.457262, 160 2.452824, 2.448678, 2.444794, 2.441150, 2.437723, 2.434494, 2.431447, 2.428568, 2.425841, 2.423257, 161 2.420803, 2.418470, 2.416250, 2.414134, 2.412116, 2.410188, 2.408345, 2.406581, 2.404892, 2.403272, 162 2.401718, 2.400225, 2.398790, 2.397410, 2.396081, 2.394801, 2.393568, 2.392377, 2.391229, 2.390119, 163 2.389047, 2.388011, 2.387008, 2.386037, 2.385097, 2.384186, 2.383302, 2.382446, 2.381615, 2.380807, 164 2.380024, 2.379262, 2.378522, 2.377802, 2.377102, 2.376420, 2.375757, 2.375111, 2.374482, 2.373868, 165 2.373270, 2.372687, 2.372119, 2.371564, 2.371022, 2.370493, 2.369977, 2.369472, 2.368979, 2.368497, 166 2.368026, 2.367566, 2.367115, 2.366674, 2.366243, 2.365821, 2.365407, 2.365002, 2.364606, 2.364217, 167 // 110 - 300 step 10 168 2.360726, 2.357825, 2.355375, 2.353278, 2.351465, 2.349880, 2.348483, 2.347243, 2.346134, 2.345137, 169 2.344236, 2.343417, 2.342670, 2.341985, 2.341356, 2.340775, 2.340238, 2.339739, 2.339275, 2.338842, 170 // 400 - 1300 step 100 171 2.335706, 2.333829, 2.332579, 2.331687, 2.331018, 2.330498, 2.330083, 2.329743, 2.329459, 2.329220, 172 // Infinity 173 2.326348], 174 }; 175 176 })(); 177 178 if (typeof module != 'undefined') { 179 for (var key in Statistics) 180 module.exports[key] = Statistics[key]; 181 } 182
