time-to-botec/squiggle/node_modules/@stdlib/math/base/special/boxcox/README.md

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@license Apache-2.0
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# boxcox
> Compute a one-parameter [Box-Cox transformation][box-cox-transformation].
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The 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^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \ln(y) & \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^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \ln(y) & \textrm{if}\ \lambda = 0 \end{cases}" data-equation="eq:boxcox_transformation_one_parameter">
<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@1cd982bdbe87913bbb66e9d6a79b0acb0fb89616/lib/node_modules/@stdlib/math/base/special/boxcox/docs/img/equation_boxcox_transformation_one_parameter.svg" alt="One-Parameter Box-Cox Transformation" />
<br>
</div>
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</section>
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<section class="usage">
## Usage
```javascript
var boxcox = require( '@stdlib/math/base/special/boxcox' );
```
#### boxcox( x, lambda )
Computes a one-parameter [Box-Cox transformation][box-cox-transformation].
```javascript
var v = boxcox( 1.0, 2.5 );
// returns 0.0
v = boxcox( 4.0, 2.5 );
// returns 12.4
v = boxcox( 10.0, 2.5 );
// returns ~126.0911
v = boxcox( 2.0, 0.0 );
// returns ~0.6931
v = boxcox( -1.0, 2.5 );
// returns NaN
v = boxcox( 0.0, -1.0 );
// returns -Infinity
```
</section>
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<section class="examples">
## Examples
<!-- eslint no-undef: "error" -->
```javascript
var incrspace = require( '@stdlib/array/incrspace' );
var boxcox = require( '@stdlib/math/base/special/boxcox' );
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 = boxcox( x[ i ], l[ j ] );
console.log( 'boxcox(%d, %d) = %d', x[ i ], l[ j ], b );
}
}
```
</section>
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## 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]: 21152. <http://www.jstor.org/stable/2984418>.
</section>
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[box-cox-transformation]: https://en.wikipedia.org/wiki/Power_transform#Box-Cox_transformation
</section>
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