95 lines
2.2 KiB
Markdown
95 lines
2.2 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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# Kernel Betaincinv
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> Inverse of the lower [incomplete beta function][incomplete-beta-function].
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<section class="intro">
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var kernelBetaincinv = require( '@stdlib/math/base/special/kernel-betaincinv' );
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```
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#### kernelBetaincinv( a, b, p, q )
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Inverts the lower regularized [incomplete beta function][incomplete-beta-function] at `a > 0` and `b > 0`. Input probabilities `p` and `q` must satisfy `p = 1 - q`. The function returns a two-element array holding the function value `y` and `1-y`.
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```javascript
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var y = kernelBetaincinv( 3.0, 3.0, 0.2, 0.8 );
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// returns [ ~0.327, ~0.673 ]
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y = kernelBetaincinv( 3.0, 3.0, 0.4, 0.6 );
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// returns [ ~0.446, ~0.554 ]
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y = kernelBetaincinv( 1.0, 6.0, 0.4, 0.6 );
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// returns [ ~0.082, ~0.918 ]
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y = kernelBetaincinv( 1.0, 6.0, 0.8, 0.2 );
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// returns [ ~0.235, ~0.765 ]
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```
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</section>
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<!-- /.usage -->
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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 randu = require( '@stdlib/random/base/randu' );
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var kernelBetaincinv = require( '@stdlib/math/base/special/kernel-betaincinv' );
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var i;
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var p;
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var a;
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var b;
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for ( i = 0; i < 100; i++ ) {
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p = randu();
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a = randu() * 10.0;
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b = randu() * 10.0;
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console.log( 'p: %d, \t a: %d, \t b: %d, \t f(p,a,b): %d', p.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), kernelBetaincinv( a, b, p, 1.0-p )[ 0 ] );
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}
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```
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</section>
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<!-- /.examples -->
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<section class="links">
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[incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function
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</section>
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<!-- /.links -->
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