Statistics

(static) TheilSenRegression(coords) → {Array}

The Theil-Sen estimator can be used to determine a more robust linear regression of a set of sample points than least squares regression in JXG.Math.Numerics.regressionPolynomial.

If the function should be applied to an array a of points, a the coords array can be generated with JavaScript array.map:

JXG.Math.Statistics.TheilSenRegression(a.map(el => el.coords));

Example

var board = JXG.JSXGraph.initBoard('jxgbox', { boundingbox: [-6,6,6,-6], axis : true });
var a=[];
a[0]=board.create('point', [0,0]);
a[1]=board.create('point', [3,0]);
a[2]=board.create('point', [0,3]);

board.create('line', [
    () => JXG.Math.Statistics.TheilSenRegression(a.map(el => el.coords))
  ],
  {strokeWidth:1, strokeColor:'black'});

Parameters

Returns

Type

Array

Details

Source

math/statistics.js, line 665

(static) abs(arr) → {Array|Number}

Determines the absolute value of every given value.

Parameters

Returns

Type

Array | Number

Details

Source

math/statistics.js, line 369

(static) add(arr1, arr2) → {Array|Number}

Adds up two (sequences of) values. If one value is an array and the other one is a number the number is added to every element of the array. If two arrays are given and the lengths don't match the shortest length is taken.

Parameters

Returns

Type

Array | Number

Details

Source

math/statistics.js, line 400

(static) boxplot(arr, coefopt) → {Array}

Compute the quartiles for the boxplot element, i.e. [min, 25% quartile, median 75% quartile, max, outliers]. NaN entries are ignored. Data array arr need not be sorted.

Parameters

Returns

Type

Array

Details

See

• Boxplot

Source

math/statistics.js, line 207

(static) div(arr1, arr2) → {Array|Number}

Divides two (sequences of) values. If two arrays are given and the lengths don't match the shortest length is taken.

Parameters

Returns

Type

Array | Number

Details

Source

math/statistics.js, line 441

(static) divide()

Details

Deprecated

Use JXG.Math.Statistics.div instead.

Source

math/statistics.js, line 479

(static) generateGaussian(mean, stdDev) → {Number}

Generate values of a standard normal random variable with the Marsaglia polar method, see https://en.wikipedia.org/wiki/Marsaglia_polar_method. See also D. E. Knuth, The art of computer programming, vol 2, p. 117.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 700

(static) histogram(x, opt)

Compute the histogram of a dataset. Optional parameters can be supplied through a JavaScript object with the following default values:

{
  bins: 10,          // Number of bins
  range: false,      // false or array. The lower and upper range of the bins.
                     // If not provided, range is simply [min(x), max(x)].
                     // Values outside the range are ignored.
  density: false,    // If true, normalize the counts by dividing by sum(counts)
  cumulative: false
}

The function returns an array containing two arrays. The first array is of length bins+1 containing the start values of the bins. The last entry contains the end values of the last bin.

The second array contains the counts of each bin.

Example

let board = JXG.JSXGraph.initBoard('jxgbox',
      { boundingbox: [-1.7, .5, 20, -.03], axis: true});
 let board2 = JXG.JSXGraph.initBoard('jxgbox2',
      { boundingbox: [-1.6, 1.1, 20, -.06], axis: true});

  let runs = [
      [0.5, 1.0, 'brown'],
      [1.0, 2.0, 'red'],
      [2.0, 2.0, 'orange'],
      [3.0, 2.0, 'yellow'],
      [5.0, 1.0, 'green'],
      [9.0, 0.5, 'black'],
      [7.5, 1.0, 'purple'],
  ]

  let labelY = .4
  runs.forEach((run,i) => {
      board.create('segment',[[7,labelY-(i/50)],[9,labelY-(i/50)]],{strokeColor:run[2]})
      board.create('text',[10,labelY-(i/50),`k=${run[0]}, θ=${run[1]}`])

      // density
      let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomGamma(run[0],run[1]))
      let res = JXG.Math.Statistics.histogram(x, { bins: 50, density: true, cumulative: false, range: [0, 20] });
      board.create('curve', [res[1], res[0]], { strokeColor: run[2], strokeWidth:2});

      // cumulative density
      res = JXG.Math.Statistics.histogram(x, { bins: 50, density: true, cumulative: true, range: [0, 20] });
      res[0].unshift(0)  // add zero to front so cumulative starts at zero
      res[1].unshift(0)
      board2.create('curve', [res[1], res[0]], { strokeColor: run[2], strokeWidth:2 });
  });

Parameters

Returns

Details

Source

math/statistics.js, line 1421

(static) max(arr) → {Number}

Extracts the maximum value from the array.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 337

(static) mean(arr) → {Number}

Determines the mean value of the values given in an array.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 86

(static) median(arr) → {Number}

The median of a finite set of values is the value that divides the set into two equal sized subsets.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 101

(static) min(arr) → {Number}

Extracts the minimum value from the array.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 349

(static) mod(arr1, arr2, mathopt) → {Array|Number}

Divides two (sequences of) values and returns the remainder. If two arrays are given and the lengths don't match the shortest length is taken.

Parameters

Returns

Type

Array | Number

Details

Source

math/statistics.js, line 493

(static) multiply(arr1, arr2) → {Array|Number}

Multiplies two (sequences of) values. If one value is an array and the other one is a number the number is multiplied to every element of the array. If two arrays are given and the lengths don't match the shortest length is taken.

Parameters

Returns

Type

Array | Number

Details

Source

math/statistics.js, line 544

(static) percentile(arr, percentile) → {Number|Array}

The P-th percentile ( \(0 < P \leq 100\) ) of a list of \(N\) ordered values (sorted from least to greatest) is the smallest value in the list such that no more than \(P\) percent of the data is strictly less than the value and at least \(P\) percent of the data is less than or equal to that value. See https://en.wikipedia.org/wiki/Percentile.

Here, the linear interpolation between closest ranks method is used.

Parameters

Returns

Type

Number | Array

Details

Source

math/statistics.js, line 158

(static) prod(arr) → {Number}

Multiplies all elements of the given array.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 69

(static) randomBeta(alpha, beta)

Generate value of a random variable with beta distribution with shape parameters alpha and beta. See https://en.wikipedia.org/wiki/Beta_distribution.

Parameters

Returns

Details

Source

math/statistics.js, line 986

(static) randomBinomial(n, p)

Generate values for a random variable in binomial distribution with parameters \(n\) and \(p\). See https://en.wikipedia.org/wiki/Binomial_distribution. It uses algorithm BG from https://dl.acm.org/doi/pdf/10.1145/42372.42381.

Example

let board = JXG.JSXGraph.initBoard('jxgbox',
    { boundingbox: [-1.7, .5, 30, -.03], axis: true });

let runs = [
    [0.5, 20, 'blue'],
    [0.7, 20, 'green'],
    [0.5, 40, 'red'],
];

let labelY = .4;
runs.forEach((run, i) => {
    board.create('segment', [[7, labelY - (i / 50)], [9, labelY - (i / 50)]], { strokeColor: run[2] });
    board.create('text', [10, labelY - (i / 50), `p=${run[0]}, n=${run[1]}`]);

    let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomBinomial(run[1], run[0]));
    let res = JXG.Math.Statistics.histogram(x, {
        bins: 40,
        density: true,
        cumulative: false,
        range: [0, 40]
    });
    board.create('curve', [res[1], res[0]], { strokeColor: run[2] });
});

Parameters

Returns

Details

Source

math/statistics.js, line 1120

(static) randomChisquare(k)

Generate value of a random variable with chi-square distribution with k degrees of freedom. See https://en.wikipedia.org/wiki/Chi-squared_distribution.

Parameters

Returns

Details

Source

math/statistics.js, line 1008

(static) randomExponential(lambda)

Generate value of a random variable with exponential distribution, i.e. \(f(x; \lambda) = \lambda * e^(-\lambda x)\) if \(x \geq 0\) and \(f(x; \lambda) = 0\) if \(x < 0\). See https://en.wikipedia.org/wiki/Exponential_distribution. Algorithm: D.E. Knuth, TAOCP 2, p. 128.

Example

let board = JXG.JSXGraph.initBoard('JXGbox',
      { boundingbox: [-.5, 1.5, 5, -.1], axis: true});

  let runs = [
      [0.5, 'red'],
      [1.0, 'green'],
      [1.5, 'blue'],
  ]

  let labelY = 1
  runs.forEach((run,i) => {
      board.create('segment',[[1.8,labelY-(i/20)],[2.3,labelY-(i/20)]],{strokeColor:run[1]})
      board.create('text',[2.5,labelY-(i/20),`λ=${run[0]}`])

      let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomExponential(run[0]))
      let res = JXG.Math.Statistics.histogram(x, { bins: 40, density: true, cumulative: false, range: false });
      board.create('curve', [res[1], res[0]], { strokeColor: run[1], strokeWidth:2});
  })

Parameters

Returns

Details

Source

math/statistics.js, line 845

(static) randomF(d1, d2)

Generate value of a random variable with F-distribution with d₁ and d₂ degrees of freedom. See https://en.wikipedia.org/wiki/F-distribution.

Parameters

Returns

Details

Source

math/statistics.js, line 1026

(static) randomGamma(a, bopt, topt)

Generate value of a random variable with gamma distribution of order alpha. See https://en.wikipedia.org/wiki/Gamma_distribution. Algorithm: D.E. Knuth, TAOCP 2, p. 129.

Example

let board = JXG.JSXGraph.initBoard('jxgbox',
      { boundingbox: [-1.7, .5, 20, -.03], axis: true});

  let runs = [
      [0.5, 1.0, 'brown'],
      [1.0, 2.0, 'red'],
      [2.0, 2.0, 'orange'],
      [3.0, 2.0, 'yellow'],
      [5.0, 1.0, 'green'],
      [9.0, 0.5, 'black'],
      [7.5, 1.0, 'purple'],
  ]

  let labelY = .4
  runs.forEach((run,i) => {
      board.create('segment',[[7,labelY-(i/50)],[9,labelY-(i/50)]],{strokeColor:run[2]})
      board.create('text',[10,labelY-(i/50),`k=${run[0]}, θ=${run[1]}`])

      // density
      let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomGamma(run[0],run[1]))
      let res = JXG.Math.Statistics.histogram(x, { bins: 50, density: true, cumulative: false, range: [0, 20] });
      board.create('curve', [res[1], res[0]], { strokeColor: run[2]});

  });

Parameters

Returns

Details

Source

math/statistics.js, line 925

(static) randomGeometric(p)

Generate values for a random variable in geometric distribution with probability \(p\). See https://en.wikipedia.org/wiki/Geometric_distribution.

Parameters

Returns

Details

Source

math/statistics.js, line 1194

(static) randomHypergeometric(good, bad, samples)

Generate values for a random variable in hypergeometric distribution. Samples are drawn from a hypergeometric distribution with specified parameters, good (ways to make a good selection), bad (ways to make a bad selection), and samples (number of items sampled, which is less than or equal to good + bad).

Naive implementation with runtime O(samples).

Parameters

Returns

Details

Source

math/statistics.js, line 1279

(static) randomNormal(mean, stdDev)

Generate value of a standard normal random variable with given mean and standard deviation. Alias for JXG.Math.Statistics#generateGaussian

Example

let board = JXG.JSXGraph.initBoard('JXGbox',
      { boundingbox: [-5, 1.5, 5, -.03], axis: true});

  let runs = [
      [0, 0.2, 'blue'],
      [0, 1.0, 'red'],
      [0, 5.0, 'orange'],
      [-2,0.5, 'green'],
  ]

  let labelY = 1.2
  runs.forEach((run,i) => {
      board.create('segment',[[1.0,labelY-(i/20)],[2.0,labelY-(i/20)]],{strokeColor:run[2]})
      board.create('text',[2.5,labelY-(i/20),`μ=${run[0]}, σ2=${run[1]}`])

      let x = Array(50000).fill(0).map(() => JXG.Math.Statistics.randomNormal(run[0],Math.sqrt(run[1])))  // sqrt so Std Dev, not Variance
      let res = JXG.Math.Statistics.histogram(x, { bins: 40, density: true, cumulative: false, range: false });
      board.create('curve', [res[1], res[0]], { strokeColor: run[2], strokeWidth:2});
  })

Parameters

Returns

Details

See

• JXG.Math.Statistics.generateGaussian

Source

math/statistics.js, line 777

(static) randomPareto(gamma, k)

Generate values for a random variable in Pareto distribution with shape \(\gamma\) and scale \(k\). See https://en.wikipedia.org/wiki/Pareto_distribution. Method: use inverse transformation sampling.

Parameters

Returns

Details

Source

math/statistics.js, line 1256

(static) randomPoisson(mu)

Generate values for a random variable in Poisson distribution with mean \(\mu\). See https://en.wikipedia.org/wiki/Poisson_distribution.

Parameters

Returns

Details

Source

math/statistics.js, line 1214

(static) randomT(nu)

Generate value of a random variable with Students-t-distribution with ν degrees of freedom. See https://en.wikipedia.org/wiki/Student%27s_t-distribution.

Parameters

Returns

Details

Source

math/statistics.js, line 1047

(static) randomUniform(a, b)

Generate value of a uniform distributed random variable in the interval [a, b].

Parameters

Returns

Details

Source

math/statistics.js, line 788

(static) range(arr) → {Array}

Determines the lowest and the highest value from the given array.

Parameters

Returns

Type

Array

Details

Source

math/statistics.js, line 359

(static) sd(arr) → {Number}

Determines the standard deviation which shows how much variation there is from the average value of a set of numbers.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 301

(static) subtract(arr1, arr2) → {Array|Number}

Subtracts two (sequences of) values. If two arrays are given and the lengths don't match the shortest length is taken.

Parameters

Returns

Type

Array | Number

Details

Source

math/statistics.js, line 585

(static) sum(arr) → {Number}

Sums up all elements of the given array.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 52

(static) variance(arr) → {Number}

Bias-corrected sample variance. A variance is a measure of how far a set of numbers are spread out from each other.

Parameters

Returns

Type

Number

Details

Source

math/statistics.js, line 276

(static) weightedMean(arr, w) → {Number}

Weighted mean value is basically the same as JXG.Math.Statistics.mean but here the values are weighted, i.e. multiplied with another value called weight. The weight values are given as a second array with the same length as the value array..

Parameters

Throws

If the dimensions of the arrays don't match.

Type

Error

Returns

Type

Number

Details

Source

math/statistics.js, line 315