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