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docs: improve examples of stats/base/dists/gumbel
PR-URL: #2140 Closes: #1629 --------- Co-authored-by: Philipp Burckhardt <[email protected]> Reviewed-by: Philipp Burckhardt <[email protected]>
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‎lib/node_modules/@stdlib/stats/base/dists/gumbel/README.md

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@@ -109,10 +109,59 @@ var y = dist.pdf( 2.0 );
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<!-- eslint no-undef: "error" -->
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```javascript
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var objectKeys = require( '@stdlib/utils/keys' );
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var Float64Array = require( '@stdlib/array/float64' );
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var filledarrayBy = require('@stdlib/array/filled-by');
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var mean = require( '@stdlib/stats/base/mean' );
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var variance = require( '@stdlib/stats/base/variance' );
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var stdev = require( '@stdlib/stats/base/stdev' );
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var randGumbel = require( '@stdlib/random/base/gumbel' ).factory;
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var gumbel = require( '@stdlib/stats/base/dists/gumbel' );
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console.log( objectKeys( gumbel ) );
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// Set the parameters of the Gumbel distribution:
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var mu = 30.0; // Location parameter (e.g., average annual maximum temperature in °C)
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var beta = 5.0; // Scale parameter
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// Simulate annual maximum daily temperatures over 1000 years:
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var N = 1000;
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var rgumbel = randGumbel( mu, beta );
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var maxTemperatures = filledarrayBy( N, 'float64', rgumbel );
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// Compute theoretical statistics of the Gumbel distribution:
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var theoreticalMean = gumbel.mean( mu, beta);
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var theoreticalVariance = gumbel.variance( mu, beta );
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var theoreticalStdev = gumbel.stdev( mu, beta );
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// Compute sample statistics of the simulated data:
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var sampleMean = mean( N, maxTemperatures, 1 );
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var sampleVariance = variance( N, 1, maxTemperatures, 1 ); // with Bessel's correction
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var sampleStdev = stdev( N, 1, maxTemperatures, 1 ); // with Bessel's correction
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// Display theoretical and sample statistics:
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console.log( '--- Statistical Comparison ---\n' );
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console.log( 'Mean:');
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console.log( ' Theoretical: %d°C', theoreticalMean.toFixed(2) );
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console.log( ' Sample: %d°C\n', sampleMean.toFixed(2) );
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console.log( 'Variance:');
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console.log( ' Theoretical: %d°C²', theoreticalVariance.toFixed(2) );
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console.log( ' Sample: %d°C²\n', sampleVariance.toFixed(2) );
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console.log( 'Standard Deviation:' );
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console.log( ' Theoretical: %d°C', theoreticalStdev.toFixed(2) );
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console.log( ' Sample: %d°C\n', sampleStdev.toFixed(2) );
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// Define quantile probabilities:
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var p = new Float64Array( [ 0.25, 0.5, 0.75 ] );
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var label = [ 'First Quartile', 'Median', 'Third Quartile' ];
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var theoreticalQuantiles = new Float64Array([
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gumbel.quantile( p[0], mu, beta ),
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gumbel.quantile( p[1], mu, beta ),
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gumbel.quantile( p[2], mu, beta )
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]);
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console.log( 'Quantiles:' );
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var i;
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for ( i = 0; i < p.length; i++ ) {
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console.log( label[i] + ': %d°C', theoreticalQuantiles[i].toFixed(2) );
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}
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```
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</section>

‎lib/node_modules/@stdlib/stats/base/dists/gumbel/examples/index.js

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'use strict';
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var objectKeys = require( '@stdlib/utils/keys' );
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var Float64Array = require( '@stdlib/array/float64' );
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var filledarrayBy = require('@stdlib/array/filled-by');
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var mean = require( '@stdlib/stats/base/mean' );
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var variance = require( '@stdlib/stats/base/variance' );
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var stdev = require( '@stdlib/stats/base/stdev' );
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var randGumbel = require( '@stdlib/random/base/gumbel' ).factory;
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var gumbel = require( './../lib' );
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console.log( objectKeys( gumbel ) );
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// Set the parameters of the Gumbel distribution:
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var mu = 30.0; // Location parameter (e.g., average annual maximum temperature in °C)
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var beta = 5.0; // Scale parameter
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// Simulate annual maximum daily temperatures over 1000 years:
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var N = 1000;
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var rgumbel = randGumbel( mu, beta );
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var maxTemperatures = filledarrayBy( N, 'float64', rgumbel );
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// Compute theoretical statistics of the Gumbel distribution:
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var theoreticalMean = gumbel.mean( mu, beta);
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var theoreticalVariance = gumbel.variance( mu, beta );
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var theoreticalStdev = gumbel.stdev( mu, beta );
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// Compute sample statistics of the simulated data:
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var sampleMean = mean( N, maxTemperatures, 1 );
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var sampleVariance = variance( N, 1, maxTemperatures, 1 ); // with Bessel's correction
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var sampleStdev = stdev( N, 1, maxTemperatures, 1 ); // with Bessel's correction
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// Display theoretical and sample statistics:
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console.log( '--- Statistical Comparison ---\n' );
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console.log( 'Mean:');
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console.log( ' Theoretical: %d°C', theoreticalMean.toFixed(2) );
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console.log( ' Sample: %d°C\n', sampleMean.toFixed(2) );
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console.log( 'Variance:');
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console.log( ' Theoretical: %d°C²', theoreticalVariance.toFixed(2) );
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console.log( ' Sample: %d°C²\n', sampleVariance.toFixed(2) );
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console.log( 'Standard Deviation:' );
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console.log( ' Theoretical: %d°C', theoreticalStdev.toFixed(2) );
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console.log( ' Sample: %d°C\n', sampleStdev.toFixed(2) );
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// Define quantile probabilities:
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var p = new Float64Array( [ 0.25, 0.5, 0.75 ] );
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var label = [ 'First Quartile', 'Median', 'Third Quartile' ];
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var theoreticalQuantiles = new Float64Array([
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gumbel.quantile( p[0], mu, beta ),
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gumbel.quantile( p[1], mu, beta ),
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gumbel.quantile( p[2], mu, beta )
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]);
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console.log( 'Quantiles:' );
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var i;
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for ( i = 0; i < p.length; i++ ) {
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console.log( label[i] + ': %d°C', theoreticalQuantiles[i].toFixed(2) );
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}

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