JSXGraph 1.11.0beta1 Reference

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Namespace JXG.Math.Statistics

      ↳ JXG.Math.Statistics

Defined in: statistics.js.

Parameters:

{Array|Number} arr

Returns:

{Array|Number}

Parameters:

{Array|Number} arr1

{Array|Number} arr2

Returns:

{Array|Number}

Parameters:

{Array|Number} arr1

Dividend

{Array|Number} arr2

Divisor

Returns:

{Array|Number}

Deprecated:

Use JXG.Math.Statistics.div instead.

Parameters:

{Number} mean

mean value of the normal distribution

{Number} stdDev

standard deviation of the normal distribution

Returns:

{Number} value of a standard normal random variable

{
  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
}

Parameters:

{Array} x

{Object} opt

Optional parameters

Returns:

Array [bin, counts] Array bins contains start values of bins, array counts contains the number of entries of x which are contained in each bin.

Examples:

 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:

{Array} arr

Returns:

{Number} The highest number from the array. It returns NaN if not every element could be interpreted as a number and -Infinity if an empty array is given or no element could be interpreted as a number.

Parameters:

{Array} arr

Returns:

{Number}

Parameters:

{Array} arr

The set of values.

Returns:

{Number}

Parameters:

{Array} arr

Returns:

{Number} The lowest number from the array. It returns NaN if not every element could be interpreted as a number and Infinity if an empty array is given or no element could be interpreted as a number.

Parameters:

{Array|Number} arr1

Dividend

{Array|Number} arr2

Divisor

{Boolean} math Optional, Default: false

Mathematical mod or symmetric mod? Default is symmetric, the JavaScript % operator.

Returns:

{Array|Number}

Parameters:

{Array|Number} arr1

{Array|Number} arr2

Returns:

{Array|Number}

Parameters:

{Array} arr

The set of values, need not be ordered.

{Number|Array} percentile

One or several percentiles

Returns:

{Number|Array} Depending if a number or an array is the input for percentile, a number or an array containing the percentiles is returned.

Parameters:

{Array} arr

An array of numbers.

Returns:

{Number}

Parameters:

{Number} alpha

> 0

{Number} beta

> 0

Returns:

Number

Parameters:

{Number} n

Number of trials (n >= 0)

{Number} p

Probability (0 <= p <= 1)

Returns:

Number Integer value of a random variable in binomial distribution

Examples:

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:

{Number} k

> 0

Returns:

Number

Parameters:

{Number} lambda

> 0

Returns:

Number

Examples:

 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:

{Number} d1

> 0

{Number} d2

> 0

Returns:

Number

Parameters:

{Number} a

shape, > 0

{Number} b Optional, Default: 1

scale, > 0

{Number} t Optional, Default: 0

threshold

Returns:

Number

Examples:

 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:

{Number} p

(0 <= p <= 1)

Returns:

Number

Parameters:

{Number} good

ways to make a good selection

{Number} bad

ways to make a bad selection

{Number} samples

number of items sampled

Returns:

Parameters:

{Number} mean

{Number} stdDev

Returns:

Number

See:

JXG.Math.Statistics.generateGaussian

Examples:

 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:

{Number} gamma

shape (0 < gamma)

{Number} k

scale (0 < k < x)

Returns:

Number

Parameters:

{Number} mu

(0 < mu)

Returns:

Number

Parameters:

{Number} nu

> 0

Returns:

Number

Parameters:

{Number} a

{Number} b

Returns:

Number

Parameters:

{Array} arr

Returns:

{Array} The minimum value as the first and the maximum value as the second value.

Parameters:

{Array} arr

Returns:

{Number}

Parameters:

{Array|Number} arr1

Minuend

{Array|Number} arr2

Subtrahend

Returns:

{Array|Number}

Parameters:

{Array} arr

An array of numbers.

Returns:

{Number}

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

Parameters:

{Array} coords

Array of JXG.Coords.

Returns:

{Array} A stdform array of the regression line.

Examples:

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:

{Array} arr

Returns:

{Number}

Parameters:

{Array} arr

Set of alues.

{Array} w

Weight values.

Throws:

{Error}

If the dimensions of the arrays don't match.

Returns:

{Number}