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feat: add stats/base/dists/burr-type3/logcdf
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‎lib/node_modules/@stdlib/stats/base/dists/burr-type3/logcdf/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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# Logarithm of Cumulative Distribution Function
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> [Burr (type III)][burr-distribution] distribution logarithm of [cumulative distribution function][cdf].
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<section class="intro">
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The [cumulative distribution function][cdf] for a [burr][burr-distribution] random variable is
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<!-- <equation class="equation" label="eq:burr-type3_logcdf" align="center"
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raw="F(x; c, d) = log(1 + x^{-c})*{-d}"
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alt="Logarithm of cumulative distribution function for a Burr (Type III) distribution."> -->
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```math
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F(x; alpha, beta) = log(1 + x^{-alpha})*{-beta}
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```
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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 logcdf = require( '@stdlib/stats/base/dists/burr-type3/logcdf' );
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```
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#### logcdf( x, alpha, beta )
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Evaluates the natural logarithm of the [cumulative distribution function][cdf] (CDF) for a [burr][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 = logcdf( 0.1, 1.0, 1.0 );
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// returns ~-2.398
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y = logcdf( 0.2, 2.0, 2.0 );
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// returns ~-6.516
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y = logcdf( 0.3, 3.0, 3.0 );
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// returns ~-10.916
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y = logcdf( 0.4, 4.0, 4.0 );
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// returns ~-14.76
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y = logcdf( 0.5, 1.0, 1.0 );
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// returns ~-1.099
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y = logcdf( 0.5, 2.0, 4.0 );
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// returns ~-6.438
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y = logcdf( 0.8, 0.5, 0.5 );
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// returns ~-0.375
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y = logcdf( -Infinity, 4.0, 2.0 );
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// returns NaN
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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 = logcdf( NaN, 1.0, 1.0 );
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// returns NaN
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y = logcdf( 0.0, NaN, 1.0 );
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// returns NaN
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y = logcdf( 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 = logcdf( 2.0, -1.0, 0.5 );
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// returns NaN
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y = logcdf( 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 = logcdf( 2.0, 0.5, -1.0 );
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// returns NaN
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y = logcdf( 2.0, 0.5, 0.0 );
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// returns NaN
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```
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#### logcdf.factory( alpha, beta )
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Returns a function for evaluating the natural logarithm of the [cumulative distribution function][cdf] for a [burr][burr-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).
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```javascript
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var mylogcdf = logcdf.factory( 0.5, 0.5 );
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var y = mylogcdf( 0.8 );
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// returns ~-0.375
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y = mylogcdf( 0.3 );
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// returns ~-0.519
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- In virtually all cases, using the `logpdf` or `logcdf` functions is preferable to manually computing the logarithm of the `pdf` or `cdf`, respectively, since the latter is prone to overflow and underflow.
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</section>
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<!-- /.notes -->
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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 logcdf = require( '@stdlib/stats/base/dists/burr-type3/logcdf' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var linspace = require( '@stdlib/array/linspace' );
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var alpha = linspace( EPS, 10.0, 10 );
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var beta = linspace( EPS, 10.0, 10 );
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var x = linspace( EPS, 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 = logcdf( x[i], alpha[i], beta[i] );
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console.log( 'x: %d, α: %d, β: %d, ln(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/logcdf/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2018 The Stdlib Authors.
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*
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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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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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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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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var EPS = require( '@stdlib/constants/float64/eps' );
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var pkg = require( './../package.json' ).name;
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var logcdf = require( './../lib' );
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// MAIN //
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bench( pkg, function benchmark( b ) {
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var alpha;
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var beta;
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var len;
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var x;
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var y;
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var i;
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len = 100;
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x = uniform( len, EPS, 10.0 );
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alpha = uniform( len, EPS, 100.0 );
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beta = uniform( len, EPS, 100.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = logcdf( x[ i % len ], alpha[ i % len ], beta[ i % len ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});
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bench( pkg+':factory', function benchmark( b ) {
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var mylogcdf;
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var len;
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var x;
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var y;
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var i;
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x = uniform( len, EPS, 10.0 );
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mylogcdf = logcdf.factory( 5.0, 6.0 );
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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y = mylogcdf( x[ i % len ] );
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( y ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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});

‎lib/node_modules/@stdlib/stats/base/dists/burr-type3/logcdf/benchmark/python/benchmark.scipy.py‎

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#!/usr/bin/env python
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#
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# @license Apache-2.0
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#
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# Copyright (c) 2018 The Stdlib Authors.
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#
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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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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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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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"""Benchmark scipy.stats.burr.logcdf."""
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from __future__ import print_function
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import timeit
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NAME = "burr:logcdf"
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REPEATS = 3
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ITERATIONS = 1000
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def print_version():
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"""Print the TAP version."""
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print("TAP version 13")
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def print_summary(total, passing):
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"""Print the benchmark summary.
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# Arguments
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* `total`: total number of tests
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* `passing`: number of passing tests
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"""
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print("#")
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print("1.." + str(total)) # TAP plan
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print("# total " + str(total))
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print("# pass " + str(passing))
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print("#")
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print("# ok")
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def print_results(elapsed):
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"""Print benchmark results.
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# Arguments
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* `elapsed`: elapsed time (in seconds)
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# Examples
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``` python
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python> print_results(0.131009101868)
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```
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"""
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rate = ITERATIONS / elapsed
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print(" ---")
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print(" iterations: " + str(ITERATIONS))
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print(" elapsed: " + str(elapsed))
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print(" rate: " + str(rate))
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print(" ...")
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def benchmark():
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"""Run the benchmark and print benchmark results."""
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setup = "from scipy.stats import burr; from random import random;"
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stmt = "y = burr.logcdf(random(), 100.56789, 55.54321)"
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t = timeit.Timer(stmt, setup=setup)
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print_version()
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for i in range(REPEATS):
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print("# python::" + NAME)
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elapsed = t.timeit(number=ITERATIONS)
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print_results(elapsed)
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print("ok " + str(i+1) + " benchmark finished")
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print_summary(REPEATS, REPEATS)
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def main():
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"""Run the benchmark."""
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benchmark()
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if __name__ == "__main__":
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main()

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