About

Kernel Density Estimation, generating probability density function (pdf) using triangular kernel, optimized to run in O(N + K).

Where:

• N: number of elements in the sample.
• K: number of points to represent the pdf.

API

create(arr, options)

Create pdf with given array and options.

Options:

• min: min value for the pdf's x range. If resulting pdf won't fit, the pdf's left part will be squeezed, as described here. Defaults to smallest value in the array minus some threshold.
• max: max value for the pdf's x range. If resulting pdf won't fit, the pdf's right will be squeezed. Defaults to largest value in the array plus some threshold.
• size: number of points to represent the pdf. Defaults to 50.
• width: determine how many points to the left and right does an element affect, similar to bandwidth in kernel density estimation. Defaults to 2.

 var arr = [1, 2, 3, 3, 4, 5, 5, 5, 6, 8, 9, 9];
var options = {
  min: 0,
  max: 10,
  size: 12,
  width: 2
};

var pdf = pdfast.create(arr, options);

pdf's value:

[ { x: 0, y: 0.020833333333333332 },
  { x: 0.9090909090909091, y: 0.0625 },
  { x: 1.8181818181818181, y: 0.10416666666666667 },
  { x: 2.727272727272727, y: 0.125 },
  { x: 3.6363636363636362, y: 0.14583333333333334 },
  { x: 4.545454545454545, y: 0.16666666666666666 },
  { x: 5.454545454545454, y: 0.10416666666666667 },
  { x: 6.363636363636363, y: 0.041666666666666664 },
  { x: 7.2727272727272725, y: 0.08333333333333333 },
  { x: 8.181818181818182, y: 0.10416666666666667 },
  { x: 9.09090909090909, y: 0.041666666666666664 },
  { x: 10, y: 0 } ]

getExpectedValueFromPdf(pdf)

 expect(
  pdfast.getExpectedValueFromPdf([
    {x: 1, y: 0.2},
    {x: 2, y: 0.3},
    {x: 3, y: 0.3},
    {x: 4, y: 0.2},
    {x: 5, y: 0.0}
  ])
).closeTo(2.5, 1e-8);

getXWithLeftTailArea(pdf, area)

 var pdf = [
  {x: 1, y: 0.2},
  {x: 2, y: 0.4},
  {x: 3, y: 0.3},
  {x: 4, y: 0.075},
  {x: 5, y: 0.025}
];

expect(pdfast.getXWithLeftTailArea(pdf, 0)).equal(1);
expect(pdfast.getXWithLeftTailArea(pdf, 0.12)).equal(1);
expect(pdfast.getXWithLeftTailArea(pdf, 0.19)).equal(1);
expect(pdfast.getXWithLeftTailArea(pdf, 0.21)).equal(2);
expect(pdfast.getXWithLeftTailArea(pdf, 0.95)).equal(4);
expect(pdfast.getXWithLeftTailArea(pdf, 1)).equal(5);

getPerplexity(pdf)

 expect(
  pdfast.getPerplexity([
    {x: 1, y: 0.2},
    {x: 2, y: 0.4},
    {x: 3, y: 0.3},
    {x: 4, y: 0.075},
    {x: 5, y: 0.025}
  ])
).closeTo(3.8041316039860336, EPS);

getUnifiedMinMax(arr, options)

Takes the same options as create. Returns an object with key min and max.

If you left min or max or both to be non number, it will be filled with number which will fit the data distribution.

getUnifiedMinMaxMulti([arr1, arr2, ...], options)

Similar with getUnifiedMinMax, but takes list of arrays. The generated min and/or max will fit all the arrays' distribution.

Useful when trying to generate pdf for multiple labelled data and want to display them in the same chart. With same min and max, one can combine the pdf correctly.

License

MIT