132 lines
2.7 KiB
Markdown
132 lines
2.7 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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# betainc
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> [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 betainc = require( '@stdlib/math/base/special/betainc' );
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```
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#### betainc( x, a, b\[, regularized\[, upper]] )
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By default, evaluates the regularized lower [incomplete beta function][incomplete-beta-function] for inputs `x`, `a > 0` and `b > 0`. The fourth and fifth parameters of the function can be used to specify whether instead to evaluate the non-regularized and/or upper incomplete beta functions, respectively.
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```javascript
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var y = betainc( 0.5, 2.0, 2.0 );
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// returns 0.5
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y = betainc( 0.5, 2.0, 2.0, false );
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// returns ~0.083
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y = betainc( 0.2, 1.0, 2.0 );
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// returns 0.36
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y = betainc( 0.2, 1.0, 2.0, true, true );
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// returns 0.64
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```
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If provided `NaN` as any argument, the function returns `NaN`.
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```javascript
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var y = betainc( NaN, 1.0, 1.0 );
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// returns NaN
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y = betainc( 0.8, NaN, 1.0 );
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// returns NaN
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y = betainc( 0.8, 1.0, NaN );
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// returns NaN
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```
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If provided a `x` outside the interval `[0,1]`, the function returns `NaN`.
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```javascript
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var y = betainc( 1.5, 1.0, 1.0 );
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// returns NaN
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y = betainc( -0.5, 1.0, 1.0 );
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// returns NaN
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```
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If provided a negative `a`, the function returns `NaN`.
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```javascript
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var y = betainc( 0.5, -2.0, 2.0 );
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// returns NaN
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```
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If provided a negative `b`, the function returns `NaN`.
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```javascript
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var y = betainc( 0.5, 2.0, -2.0 );
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// returns NaN
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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 betainc = require( '@stdlib/math/base/special/betainc' );
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var i;
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var x;
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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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x = randu();
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a = randu() * 10.0;
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b = randu() * 10.0;
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console.log( 'x: %d, \t a: %d, \t b: %d, \t f(x,a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), betainc( x, a, b ).toFixed( 4 ) );
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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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