pdfast

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 bandwith 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);

License

MIT