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feat: add stats/base/dists/burr-type3/cdf
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‎lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/README.md‎

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<!--
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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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# Cumulative Distribution Function
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> [Burr (type III)][burr-distribution] distribution [cumulative distribution function][cdf].
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<section class="intro">
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The [cumulative distribution function][cdf] for a [Burr (type III)][burr-distribution] random variable is
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<!-- <equation class="equation" label="eq:burr-type3_cdf" align="center"
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raw="F(x; c, d) = (1 + x^{-c})^{-d}"
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alt="Cumulative distribution function for a Burr (Type III) distribution."> -->
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```math
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F(x; alpha, beta) = (1 + x^{-alpha})^{-beta}
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```
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<!-- <div class="equation" align="center" data-raw-text="F(x;c,d) = (1 + x^{-c})^{-d}" data-equation="eq:burr-type3_cdf">
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<img src="https://quicklatex.com/cache3/1e/ql_96e6c56a3c01ce5db3f378b28ee9511e_l3.png" alt="Cumulative distribution function for a Burr (Type III) distribution.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `alpha > 0` is the first shape parameter and `beta > 0` is the second shape parameter.
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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 cdf = require( '@stdlib/stats/base/dists/burr-type3/cdf' );
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```
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#### cdf( x, alpha, beta )
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Evaluates the [cumulative distribution function][cdf] (CDF) for a [Burr (type III)][burr-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
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```javascript
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var y = cdf( 0.1, 1.0, 1.0 );
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// returns ~0.09
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y = cdf( 0.2, 2.0, 2.0 );
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// returns ~0.0015
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y = cdf( 0.4, 4.0, 4.0 );
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// returns ~3.88e-7
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y = cdf( 1.0, 0.1, 1.0 );
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// returns 0.5
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y = cdf( 0.3, 0.5, 0.5 );
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// returns ~0.59
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y = cdf( 0.5, 1.0, 1.0 );
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// returns ~0.33
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y = cdf( 0.5, 2.0, 4.0 );
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// returns ~0.0016
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y = cdf( 0.8, 0.5, 0.5 );
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// returns ~0.69
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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 = cdf( NaN, 1.0, 1.0 );
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// returns NaN
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y = cdf( 0.0, NaN, 1.0 );
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// returns NaN
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y = cdf( 0.0, 1.0, NaN );
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// returns NaN
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```
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If provided `alpha <= 0`, the function returns `NaN`.
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```javascript
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var y = cdf( 2.0, -1.0, 0.5 );
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// returns NaN
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y = cdf( 2.0, 0.0, 0.5 );
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// returns NaN
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```
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If provided `beta <= 0`, the function returns `NaN`.
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```javascript
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var y = cdf( 2.0, 0.5, -1.0 );
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// returns NaN
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y = cdf( 2.0, 0.5, 0.0 );
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// returns NaN
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```
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#### cdf.factory( alpha, beta )
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Returns a function for evaluating the [cumulative distribution function][cdf] for a [Burr (type III)][burr-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
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```javascript
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var mycdf = cdf.factory( 0.5, 0.5 );
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var y = mycdf( 0.8 );
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// returns ~0.69
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y = mycdf( 0.3 );
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// returns ~0.59
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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 cdf = require( '@stdlib/stats/base/dists/burr-type3/cdf' );
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var linspace = require( '@stdlib/array/linspace' );
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var alpha = linspace( 1, 10.0, 10 );
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var beta = linspace( 1, 10.0, 10 );
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var x = linspace( 0.1, 1.0, 10 );
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var y;
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var i;
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for ( i = 0; i < 10; i++ ) {
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y = cdf( x[ i ], alpha[ i ], beta[ i ] );
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console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x[i].toFixed( 4 ), alpha[i].toFixed( 4 ), beta[i].toFixed( 4 ), y.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 for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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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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[burr-distribution]: https://en.wikipedia.org/wiki/Burr_distribution
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[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/examples/index.js‎

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for ( i = 0; i < 10; i++ ) {
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y = cdf( x[ i ], alpha[ i ], beta[ i ] );
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console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x[i].toFixed( 4 ), alpha[i].toFixed( 4 ), beta[i].toFixed( 4 ), y );
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console.log( 'x: %d, α: %d, β: %d, F(x;α,β): %d', x[i].toFixed( 4 ), alpha[i].toFixed( 4 ), beta[i].toFixed( 4 ), y.toFixed( 4 ) );
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}

‎lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/test/test.cdf.js‎

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t.equal( y, expected[i], 'x: '+x[i]+'. c:'+c[i]+'. d:'+d[i]+', y: '+y+', expected: '+expected[i] );
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} else {
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delta = abs( y - expected[ i ] );
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tol = 2 * EPS * abs( expected[ i ] );
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tol = 2.0 * EPS * abs( expected[ i ] );
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t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. c: '+c[i]+'. d: '+d[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
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}
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}
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t.equal( y, expected[i], 'x: '+x[i]+'. c:'+c[i]+'. d:'+d[i]+', y: '+y+', expected: '+expected[i] );
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} else {
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delta = abs( y - expected[ i ] );
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tol = 5 * EPS * abs( expected[ i ] );
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tol = 5.0 * EPS * abs( expected[ i ] );
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t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. c: '+c[i]+'. d: '+d[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
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}
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t.equal( y, expected[i], 'x: '+x[i]+'. c: '+c[i]+'. d: '+d[i]+', y: '+y+', expected: '+expected[i] );
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} else {
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delta = abs( y - expected[ i ] );
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tol = 12 * EPS * abs( expected[ i ] );
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tol = 12.0 * EPS * abs( expected[ i ] );
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t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. c: '+c[i]+'. d: '+d[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
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}
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}

‎lib/node_modules/@stdlib/stats/base/dists/burr-type3/cdf/test/test.factory.js‎

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t.end();
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});
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tape( 'the created function evaluates the cdf for `x` given small `c` and `d`', function test( t ) {
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tape( 'the created function evaluates the cdf for `x` given small parameters `c` and `d`', function test( t ) {
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tape( 'the created function evaluates the cdf for `x` given a medium `c`', function test( t ) {
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tape( 'the created function evaluates the cdf for `x` given medium parameters `c` and `d`', function test( t ) {
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t.equal( y, expected[i], 'x: '+x[i]+'. c: '+c[i]+'. d: '+d[i]+', y: '+y+', expected: '+expected[i] );
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tol = 5.0 * EPS * abs( expected[ i ] );
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t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. c: '+c[i]+'. d: '+d[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
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t.end();
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});
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tape( 'the created function evaluates the cdf for `x` given a large `c`', function test( t ) {
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tape( 'the created function evaluates the cdf for `x` given large parameters `c` and `d`', function test( t ) {
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t.equal( y, expected[i], 'x: '+x[i]+'. c: '+c[i]+'. d: '+d[i]+', y: '+y+', expected: '+expected[i] );
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tol = 12.0 * EPS * abs( expected[ i ] );
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t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. c: '+c[i]+'. d: '+d[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' );
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}
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}

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