136 lines
3.8 KiB
Markdown
136 lines
3.8 KiB
Markdown
|
<!--
|
|||
|
|
|
|||
|
|
@license Apache-2.0
|
|||
|
|
|
|||
|
|
Copyright (c) 2018 The Stdlib Authors.
|
|||
|
|
|
|||
|
|
Licensed under the Apache License, Version 2.0 (the "License");
|
|||
|
|
you may not use this file except in compliance with the License.
|
|||
|
|
You may obtain a copy of the License at
|
|||
|
|
|
|||
|
|
http://www.apache.org/licenses/LICENSE-2.0
|
|||
|
|
|
|||
|
|
Unless required by applicable law or agreed to in writing, software
|
|||
|
|
distributed under the License is distributed on an "AS IS" BASIS,
|
|||
|
|
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|||
|
|
See the License for the specific language governing permissions and
|
|||
|
|
limitations under the License.
|
|||
|
|
|
|||
|
|
-->
|
|||
|
|
|
|||
|
|
# boxcox1p
|
|||
|
|
|
|||
|
|
> Compute a one-parameter [Box-Cox transformation][box-cox-transformation] of `1+x`.
|
|||
|
|
|
|||
|
|
<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
|
|||
|
|
|
|||
|
|
<section class="intro">
|
|||
|
|
|
|||
|
|
A one-parameter [Box-Cox transformation][box-cox-transformation] is defined as
|
|||
|
|
|
|||
|
|
<!-- <equation class="equation" label="eq:boxcox_transformation_one_parameter" align="center" raw="y^{\lambda} = \begin{cases}\frac{(y + 1)^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \log(y + 1) & \textrm{if}\ \lambda = 0 \end{cases}" alt="One-Parameter Box-Cox Transformation"> -->
|
|||
|
|
|
|||
|
|
<div class="equation" align="center" data-raw-text="y^{\lambda} = \begin{cases}\frac{(y + 1)^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \log(y + 1) & \textrm{if}\ \lambda = 0 \end{cases}" data-equation="eq:boxcox_transformation_one_parameter">
|
|||
|
|
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@cd43faf7aaac9e3059ef876713c9433ea6f3818d/lib/node_modules/@stdlib/math/base/special/boxcox1p/docs/img/equation_boxcox_transformation_one_parameter.svg" alt="One-Parameter Box-Cox Transformation" />
|
|||
|
|
<br>
|
|||
|
|
</div>
|
|||
|
|
|
|||
|
|
<!-- </equation> -->
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
<!-- /.intro -->
|
|||
|
|
|
|||
|
|
<!-- Package usage documentation. -->
|
|||
|
|
|
|||
|
|
<section class="usage">
|
|||
|
|
|
|||
|
|
## Usage
|
|||
|
|
|
|||
|
|
```javascript
|
|||
|
|
var boxcox1p = require( '@stdlib/math/base/special/boxcox1p' );
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
#### boxcox1p( x, lambda )
|
|||
|
|
|
|||
|
|
Computes a one-parameter [Box-Cox transformation][box-cox-transformation] of `1+x`.
|
|||
|
|
|
|||
|
|
```javascript
|
|||
|
|
var v = boxcox1p( 1.0, 2.5 );
|
|||
|
|
// returns ~1.8627
|
|||
|
|
|
|||
|
|
v = boxcox1p( 4.0, 2.5 );
|
|||
|
|
// returns ~21.9607
|
|||
|
|
|
|||
|
|
v = boxcox1p( 10.0, 2.5 );
|
|||
|
|
// returns ~160.1246
|
|||
|
|
|
|||
|
|
v = boxcox1p( 2.0, 0.0 );
|
|||
|
|
// returns ~1.0986
|
|||
|
|
|
|||
|
|
v = boxcox1p( -1.0, 2.5 );
|
|||
|
|
// returns -0.4
|
|||
|
|
|
|||
|
|
v = boxcox1p( 0.0, -1.0 );
|
|||
|
|
// returns 0.0
|
|||
|
|
|
|||
|
|
v = boxcox1p( -1.0, -1.0 );
|
|||
|
|
// returns -Infinity
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
<!-- /.usage -->
|
|||
|
|
|
|||
|
|
<!-- Package usage examples. -->
|
|||
|
|
|
|||
|
|
<section class="examples">
|
|||
|
|
|
|||
|
|
## Examples
|
|||
|
|
|
|||
|
|
<!-- eslint no-undef: "error" -->
|
|||
|
|
|
|||
|
|
```javascript
|
|||
|
|
var incrspace = require( '@stdlib/array/incrspace' );
|
|||
|
|
var boxcox1p = require( '@stdlib/math/base/special/boxcox1p' );
|
|||
|
|
|
|||
|
|
var x = incrspace( -1.0, 10.0, 1.0 );
|
|||
|
|
var l = incrspace( -0.5, 5.0, 0.5 );
|
|||
|
|
var b;
|
|||
|
|
var i;
|
|||
|
|
var j;
|
|||
|
|
|
|||
|
|
for ( i = 0; i < x.length; i++ ) {
|
|||
|
|
for ( j = 0; j < l.length; j++ ) {
|
|||
|
|
b = boxcox1p( x[ i ], l[ j ] );
|
|||
|
|
console.log( 'boxcox1p(%d, %d) = %d', x[ i ], l[ j ], b );
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
<!-- /.examples -->
|
|||
|
|
|
|||
|
|
<!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
|
|||
|
|
|
|||
|
|
<section class="references">
|
|||
|
|
|
|||
|
|
## References
|
|||
|
|
|
|||
|
|
- Box, G. E. P., and D. R. Cox. 1964. "An Analysis of Transformations." _Journal of the Royal Statistical Society. Series B (Methodological)_ 26 (2). \[Royal Statistical Society, Wiley]: 211–52. <http://www.jstor.org/stable/2984418>.
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
<!-- /.references -->
|
|||
|
|
|
|||
|
|
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
|
|||
|
|
|
|||
|
|
<section class="links">
|
|||
|
|
|
|||
|
|
[box-cox-transformation]: https://en.wikipedia.org/wiki/Power_transform#Box-Cox_transformation
|
|||
|
|
|
|||
|
|
</section>
|
|||
|
|
|
|||
|
|
<!-- /.links -->
|