time-to-botec

Benchmark sampling in different programming languages
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README.md (3085B)

      1 <!--
      2 
      3 @license Apache-2.0
      4 
      5 Copyright (c) 2018 The Stdlib Authors.
      6 
      7 Licensed under the Apache License, Version 2.0 (the "License");
      8 you may not use this file except in compliance with the License.
      9 You may obtain a copy of the License at
     10 
     11    http://www.apache.org/licenses/LICENSE-2.0
     12 
     13 Unless required by applicable law or agreed to in writing, software
     14 distributed under the License is distributed on an "AS IS" BASIS,
     15 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
     16 See the License for the specific language governing permissions and
     17 limitations under the License.
     18 
     19 -->
     20 
     21 # betaincinv
     22 
     23 > Inverse of the [incomplete beta function][incomplete-beta-function].
     24 
     25 <section class="intro">
     26 
     27 </section>
     28 
     29 <!-- /.intro -->
     30 
     31 <section class="usage">
     32 
     33 ## Usage
     34 
     35 ```javascript
     36 var betaincinv = require( '@stdlib/math/base/special/betaincinv' );
     37 ```
     38 
     39 #### betaincinv( p, a, b\[, upper] )
     40 
     41 Inverts the regularized [incomplete beta function][incomplete-beta-function]. Contrary to the more commonly used definition, in this implementation the first parameter is the probability `p` and the second and third parameter are `a` and `b`. By default, the function inverts the _lower_ regularized [incomplete beta function][incomplete-beta-function]. To invert the _upper_ function instead, set the `upper` argument to `true`.
     42 
     43 ```javascript
     44 var y = betaincinv( 0.2, 3.0, 3.0 );
     45 // returns ~0.327
     46 
     47 y = betaincinv( 0.4, 3.0, 3.0 );
     48 // returns ~0.446
     49 
     50 y = betaincinv( 0.4, 3.0, 3.0, true );
     51 // returns ~0.554
     52 
     53 y = betaincinv( 0.4, 1.0, 6.0 );
     54 // returns ~0.082
     55 
     56 y = betaincinv( 0.8, 1.0, 6.0 );
     57 // returns ~0.235
     58 ```
     59 
     60 If provided `NaN` as any argument, the function returns `NaN`.
     61 
     62 ```javascript
     63 var y = betaincinv( NaN, 1.0, 1.0 );
     64 // returns NaN
     65 
     66 y = betaincinv( 0.5, NaN, 1.0 );
     67 // returns NaN
     68 
     69 y = betaincinv( 0.5, 1.0, NaN );
     70 // returns NaN
     71 ```
     72 
     73 If provided a value outside `[0,1]` for `p`, the function returns `NaN`.
     74 
     75 ```javascript
     76 var y = betaincinv( 1.2, 1.0, 1.0 );
     77 // returns NaN
     78 
     79 y = betaincinv( -0.5, 1.0, 1.0 );
     80 // returns NaN
     81 ```
     82 
     83 If provided a nonpositive `a`, the function returns `NaN`.
     84 
     85 ```javascript
     86 var y = betaincinv( 0.5, -2.0, 2.0 );
     87 // returns NaN
     88 
     89 y = betaincinv( 0.5, 0.0, 2.0 );
     90 // returns NaN
     91 ```
     92 
     93 If provided a nonpositive `b`, the function returns `NaN`.
     94 
     95 ```javascript
     96 var y = betaincinv( 0.5, 2.0, -2.0 );
     97 // returns NaN
     98 
     99 y = betaincinv( 0.5, 2.0, 0.0 );
    100 // returns NaN
    101 ```
    102 
    103 </section>
    104 
    105 <!-- /.usage -->
    106 
    107 <section class="examples">
    108 
    109 ## Examples
    110 
    111 <!-- eslint no-undef: "error" -->
    112 
    113 ```javascript
    114 var randu = require( '@stdlib/random/base/randu' );
    115 var betaincinv = require( '@stdlib/math/base/special/betaincinv' );
    116 
    117 var i;
    118 var p;
    119 var a;
    120 var b;
    121 
    122 for ( i = 0; i < 100; i++ ) {
    123     p = randu();
    124     a = randu() * 10.0;
    125     b = randu() * 10.0;
    126     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 ), betaincinv( p, a, b ) );
    127 }
    128 ```
    129 
    130 </section>
    131 
    132 <!-- /.examples -->
    133 
    134 <section class="links">
    135 
    136 [incomplete-beta-function]: https://en.wikipedia.org/wiki/Incomplete_beta_function
    137 
    138 </section>
    139 
    140 <!-- /.links -->