npm package: @stdlib/stats-kde2d
Description: Two-dimensional kernel density estimation.
Author: The Stdlib Authors
Latest version: 0.2.2

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<details>
  <summary>
    About stdlib...
  </summary>
  <p>We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.</p>
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</details>

# kde2d

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Two-dimensional kernel density estimation.

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-kde2d
```

</section>

<section class="usage">

## Usage

```javascript
var kde2d = require( '@stdlib/stats-kde2d' );
```

#### kde2d( x, y\[, opts] )

By default, the function computes two-dimensional normal kernel density estimation for data provided in [arrays][mdn-array] or [typed-arrays][mdn-typed-array] `x` and `y`. When these arguments are supplied, the arrays are coerced into a Matrix-like object.

<!-- eslint-disable array-element-newline -->

```javascript
var x = [ 0.6333, 0.8643, 1.0952, 1.3262, 1.5571,
    1.7881, 2.019, 2.25, 2.481, 2.7119 ];
var y = [ -0.0468, 0.8012, 1.6492, 2.4973, 3.3454,
    4.1934, 5.0415, 5.8896, 6.7376, 7.5857 ];

var out = kde2d( x, y );
/* e.g., returns
    {
        'x': [ ~0.633, ~0.72, ... ],
        'y': [ ~-0.047, ~0.271 ... ],
        'z': ndarray{ <Float64Array>[ ~0.0455, ... ]}
    }
*/
```

#### kde2d( arr\[, opts] )

The function has the ability to handle [ndarrays][nd-array]. Specifically the `ndarray` must be constructed so that there are two columns present, the first column containing the `x` values and the second column containing the `y` values.

Note that for the output the `x` and `y` properties refer to the equally spaced gridpoints of `X` and `Y` used to calculate `z`.

<!-- eslint-disable array-element-newline -->

```javascript
var ndarray = require( '@stdlib/ndarray-ctor' );

var x = [ 0.6333, 0.8643, 1.0952, 1.3262, 1.5571,
    1.7881, 2.019, 2.25, 2.481, 2.7119 ];
var y = [ -0.0468, 0.8012, 1.6492, 2.4973, 3.3454,
    4.1934, 5.0415, 5.8896, 6.7376, 7.5857 ];

var buffer = x.concat( y );
var n = x.length;
var shape = [ n, 2 ];
var strides = [ 1, n ];
var offset = 0;
var order = 'column-major';

var arr = ndarray( 'generic', buffer, shape, strides, offset, order );

var out = kde2d( arr );
/* e.g., returns
    {
        'x': [ ~0.633, ~0.72, ... ],
        'y': [ ~-0.047,~ 0.271, ... ],
        'z': ndarray{ <Float64Array>[0.04547178438418015, ... ]}
    }
*/
```

The function accepts the following `options`:

-   **h**: `NumberArray` of length 2 indicating the X and Y bandwidth values, respectively.
-   **n**: a positive `integer` indicating the number of partitions to create in the grid. Default: `25`.
-   **xMin**: a `number` indicating the lower bound of X. Must be strictly less than `xMax`. Will default to the minimum value of `X`.
-   **xMax**: a `number` indicating the upper bound of X. Must be strictly greater than `xMin`. Will default to the maximum value of `X`.
-   **yMin**: a `number` indicating the lower bound of Y. Must be strictly less than `yMax`. Will default to the minimum value of `Y`.
-   **yMax**: a `number` indicating the upper bound of Y. Must be strictly greater than `yMin`. Will default to the maximum value of `Y`.
-   **kernel**: a `string` or `function` indicating the kernel to be used when calculating the estimation. If a `string` is supplied then it will be matched to a pre-defined kernel function. Otherwise you may supply a function to support custom kernels. Will default to the `gaussian` kernel.

By default, the bandwidth argument is set by a builtin function. To choose different bandwidth values, set the `h` option. Note that if you use a custom bandwidth for one axis, you must also use a custom bandwidth for the other axis.

<!-- eslint-disable array-element-newline -->

```javascript
var x = [ 0.6333, 0.8643, 1.0952, 1.3262, 1.5571,
    1.7881, 2.019, 2.25, 2.481, 2.7119 ];
var y = [ -0.0468, 0.8012, 1.6492, 2.4973, 3.3454,
    4.1934, 5.0415, 5.8896, 6.7376, 7.5857 ];

var out = kde2d( x, y, {
    'h': [ 0.05, 0.1 ]
});
/* e.g., returns
    {
        'x': [ 0.148, 0.3772, ... ],
        'y': [ -1.1511, -0.253, ... ],
        'z': ndarray{ <Float64Array>[ 6.344e-154, 1.93e-171, ... ]}
    }
*/
```

By default, we use `25` partitions. To change the number of partitions, set the `n` option.

<!-- eslint-disable array-element-newline -->

```javascript
var x = [ 0.6333, 0.8643, 1.0952, 1.3262, 1.5571,
    1.7881, 2.019, 2.25, 2.481, 2.7119 ];
var y = [ -0.0468, 0.8012, 1.6492, 2.4973, 3.3454,
    4.1934, 5.0415, 5.8896, 6.7376, 7.5857 ];

var out = kde2d( x, y, {
    'n': 15
});
/* e.g., returns
    {
        'x': [ 0.0623, 0.452, ... ],
        'y': [ 0.1378, 1.6266, ... ],
        'z': ndarray{ <Float64Array>[1.211e-7, 5.76e-7, ... ]}
    }
*/
```

As a default choice, the `kde2d` function sets the `xMin`, `xMax`, `yMin` and `yMax` values to be the minimum and maximum of the `X` and `Y` arrays or columns of the supplied arguments. We may change the options as follows:

<!-- eslint-disable array-element-newline -->

```javascript
var x = [ 0.6333, 0.8643, 1.0952, 1.3262, 1.5571,
    1.7881, 2.019, 2.25, 2.481, 2.7119 ];
var y = [ -0.0468, 0.8012, 1.6492, 2.4973, 3.3454,
    4.1934, 5.0415, 5.8896, 6.7376, 7.5857 ];

var out = kde2d( x, y, {
    'xMin': 0.0,
    'xMax': 2.5,
    'yMin': 0.0,
    'yMax': 6.0
});
/* e.g., returns
    {
        'x': [ 0, 0.1041, ... ],
        'y': [ 0, 0.25, ... ],
        'z': ndarray{ <Float64Array>[ 1.762e-8, 2.94e-8, ... ]}
    }
*/
```

</section>

<!-- /.usage -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var normal = require( '@stdlib/random-base-normal' );
var kde2d = require( '@stdlib/stats-kde2d' );

var randX;
var randY;
var out;
var i;
var x;
var y;
var n;

n = 100;

x = new Array( n );
y = new Array( n );

randX = normal.factory( 3.0, 1.2 );
randY = normal.factory( 10.0, 4.5 );

for ( i = 0; i < n; i++ ) {
    x[ i ] = randX();
    y[ i ] = randY();
}

out = kde2d( x, y );
/* e.g., returns
    {
        'x': [0.022, 0.2614, ...],
        'y': [-4.533, 3.602, ...],
        'z': ndarray { Float64Array [9.8266e-11, 6.45e-9, ...]}
}
*/
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

</section>

<!-- /.stdlib -->

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[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-kde2d.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-kde2d

[test-image]: https://github.com/stdlib-js/stats-kde2d/actions/workflows/test.yml/badge.svg?branch=v0.2.2
[test-url]: https://github.com/stdlib-js/stats-kde2d/actions/workflows/test.yml?query=branch:v0.2.2

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-kde2d/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-kde2d?branch=main

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[stdlib]: https://github.com/stdlib-js/stdlib

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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/stats-kde2d/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-kde2d/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-kde2d/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-kde2d/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-kde2d/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-kde2d/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-kde2d/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-kde2d/main/LICENSE

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays

[nd-array]: https://github.com/stdlib-js/stdlib/blob/develop/lib/node_modules/@stdlib/ndarray/ctor/README.md

</section>

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