139 lines
4.0 KiB
Markdown
139 lines
4.0 KiB
Markdown
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@license Apache-2.0
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Copyright (c) 2018 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# boxcox1pinv
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> Compute the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation] for `1+x`.
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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To compute the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation], one finds the `x` such that
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<!-- <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"> -->
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<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">
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<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" />
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<br>
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</div>
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<!-- </equation> -->
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</section>
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<!-- /.intro -->
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<!-- Package usage documentation. -->
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<section class="usage">
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## Usage
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```javascript
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var boxcox1pinv = require( '@stdlib/math/base/special/boxcox1pinv' );
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```
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#### boxcox1pinv( y, lambda )
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Computes the inverse of a one-parameter [Box-Cox transformation][box-cox-transformation] for `1+x`.
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```javascript
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var v = boxcox1pinv( 1.0, 2.5 );
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// returns ~0.6505
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v = boxcox1pinv( 4.0, 2.5 );
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// returns ~1.6095
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v = boxcox1pinv( 10.0, 2.5 );
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// returns ~2.6812
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v = boxcox1pinv( 2.0, 0.0 );
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// returns ~6.3891
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v = boxcox1pinv( -1.0, 2.5 );
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// returns NaN
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v = boxcox1pinv( 0.0, -1.0 );
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// returns 0.0
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v = boxcox1pinv( 1.0, NaN );
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// returns NaN
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v = boxcox1pinv( NaN, 3.1 );
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// returns NaN
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```
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</section>
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<!-- /.usage -->
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<!-- Package usage examples. -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var incrspace = require( '@stdlib/array/incrspace' );
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var boxcox1pinv = require( '@stdlib/math/base/special/boxcox1pinv' );
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var y = incrspace( -1.0, 10.0, 1.0 );
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var l = incrspace( -0.5, 5.0, 0.5 );
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var b;
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var i;
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var j;
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for ( i = 0; i < y.length; i++ ) {
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for ( j = 0; j < l.length; j++ ) {
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b = boxcox1pinv( y[ i ], l[ j ] );
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console.log( 'boxcox1pinv(%d, %d) = %d', y[ i ], l[ j ], b );
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}
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}
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```
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</section>
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<!-- /.examples -->
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<!-- 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. -->
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<section class="references">
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## References
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- 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>.
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</section>
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<!-- /.references -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[box-cox-transformation]: https://en.wikipedia.org/wiki/Power_transform#Box-Cox_transformation
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</section>
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<!-- /.links -->
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