npm package: @stdlib/math-base-special-boxcox1pinv
Description: Compute the inverse of a one-parameter Box-Cox transformation for 1+x.
Author: The Stdlib Authors
Latest version: 0.3.1

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# boxcox1pinv

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

> Compute the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation] for `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">

To compute the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation], one finds the `x` such that

<!-- <equation class="equation" label="eq:inverse_boxcox_transformation_one_parameter" align="center" raw="y^{\lambda} = \begin{cases}\frac{(x + 1)^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \log(x + 1) & \textrm{if}\ \lambda = 0 \end{cases}" alt="Inverse One-Parameter Box-Cox Transformation"> -->

<div class="equation" align="center" data-raw-text="y^{\lambda} = \begin{cases}\frac{(x + 1)^{\lambda} - 1}{\lambda} & \textrm{if}\ \lambda \neq 0 \\ \log(x + 1) & \textrm{if}\ \lambda = 0 \end{cases}" data-equation="eq:inverse_boxcox_transformation_one_parameter">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e8453b2b45eefe64cc256c32bbb826204180623d/lib/node_modules/@stdlib/math/base/special/boxcox1pinv/docs/img/equation_inverse_boxcox_transformation_one_parameter.svg" alt="Inverse One-Parameter Box-Cox Transformation" />
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<!-- Package usage documentation. -->

<section class="installation">

## Installation

```bash
npm install @stdlib/math-base-special-boxcox1pinv
```

</section>

<section class="usage">

## Usage

```javascript
var boxcox1pinv = require( '@stdlib/math-base-special-boxcox1pinv' );
```

#### boxcox1pinv( y, lambda )

Computes the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation] for `1+x`.

```javascript
var v = boxcox1pinv( 1.0, 2.5 );
// returns ~0.6505

v = boxcox1pinv( 4.0, 2.5 );
// returns ~1.6095

v = boxcox1pinv( 10.0, 2.5 );
// returns ~2.6812

v = boxcox1pinv( 2.0, 0.0 );
// returns ~6.3891

v = boxcox1pinv( -1.0, 2.5 );
// returns NaN

v = boxcox1pinv( 0.0, -1.0 );
// returns 0.0

v = boxcox1pinv( 1.0, NaN );
// returns NaN

v = boxcox1pinv( NaN, 3.1 );
// returns NaN
```

</section>

<!-- /.usage -->

<!-- Package usage examples. -->

<section class="examples">

## Examples

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

```javascript
var incrspace = require( '@stdlib/array-base-incrspace' );
var boxcox1pinv = require( '@stdlib/math-base-special-boxcox1pinv' );

var y = 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 < y.length; i++ ) {
    for ( j = 0; j < l.length; j++ ) {
        b = boxcox1pinv( y[ i ], l[ j ] );
        console.log( 'boxcox1pinv(%d, %d) = %d', y[ i ], l[ j ], b );
    }
}
```

</section>

<!-- /.examples -->

<!-- C interface documentation. -->

* * *

<section class="c">

## C APIs

<!-- 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">

</section>

<!-- /.intro -->

<!-- C usage documentation. -->

<section class="usage">

### Usage

```c
#include "stdlib/math/base/special/boxcox1pinv.h"
```

#### stdlib_base_boxcox1pinv( y, lambda )

Computes the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation] of `1+x`.

```c
double out = stdlib_base_boxcox1pinv( 1.0, 2.5 );
// returns ~0.6505

out = stdlib_base_boxcox1pinv( 4.0, 2.5 );
// returns ~1.6095
```

The function accepts the following arguments:

-   **y**: `[in] double` input value.
-   **lambda**: `[in] double` power parameter.

```c
double stdlib_base_boxcox1pinv ( const double y, const double lambda );
```

</section>

<!-- /.usage -->

<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="notes">

</section>

<!-- /.notes -->

<!-- C API usage examples. -->

<section class="examples">

### Examples

```c
#include "stdlib/math/base/special/boxcox1pinv.h"
#include <stdio.h>

int main( void ) {
    const double y[] = { -1.0, 10.0, 1.0 };
    const double l[] = { -0.5, 5.0, 0.5 };

    double b;
    int i;
    int j;
    for ( i = 0; i < 3; i++ ) {
        for ( j = 0; j < 3; j++ ){
            b = stdlib_base_boxcox1pinv( y[ i ], l[ j ] );
            printf ( "boxcox1pinv(%lf, %lf) = %lf\n", y[ i ], l[ j ], b );
        }
    }
}
```

</section>

<!-- /.examples -->

</section>

<!-- /.c -->

<!-- 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 -->

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<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/math-base/special/boxcox`][@stdlib/math/base/special/boxcox]</span><span class="delimiter">: </span><span class="description">compute a one-parameter Box-Cox transformation.</span>
-   <span class="package-name">[`@stdlib/math-base/special/boxcox1p`][@stdlib/math/base/special/boxcox1p]</span><span class="delimiter">: </span><span class="description">compute a one-parameter Box-Cox transformation of 1+x.</span>
-   <span class="package-name">[`@stdlib/math-base/special/boxcoxinv`][@stdlib/math/base/special/boxcoxinv]</span><span class="delimiter">: </span><span class="description">compute the inverse of a one-parameter Box-Cox transformation.</span>

</section>

<!-- /.related -->

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* * *

## 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].

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---

## License

See [LICENSE][stdlib-license].


## Copyright

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

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[box-cox-transformation]: https://en.wikipedia.org/wiki/Power_transform#Box-Cox_transformation

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