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docs: improve README examples of stats/base/dists/gamma namespace
PR-URL: #1804 Ref: #1627 Co-authored-by: Philipp Burckhardt <[email protected]> Co-authored-by: shivam Ahir <[email protected]> Reviewed-by: Philipp Burckhardt <[email protected]>
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‎lib/node_modules/@stdlib/stats/base/dists/gamma/README.md

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@@ -108,10 +108,91 @@ var y = dist.cdf( 0.5 );
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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 gammaRandomFactory = require( '@stdlib/random/base/gamma' ).factory;
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var filledarrayby = require( '@stdlib/array/filled-by' );
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var Float64Array = require( '@stdlib/array/float64' );
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var variance = require( '@stdlib/stats/base/variance' );
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var linspace = require( '@stdlib/array/base/linspace' );
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var mean = require( '@stdlib/stats/base/mean' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var gamma = require( '@stdlib/stats/base/dists/gamma' );
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console.log( objectKeys( gamma ) );
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// Define the shape and scale parameters:
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var alpha = 3.0; // shape parameter (α)
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var beta = 2.0; // scale parameter (β)
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// Generate an array of x values:
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var x = linspace( 0.0, 20.0, 100 );
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// Compute the PDF for each x:
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var gammaPDF = gamma.pdf.factory( alpha, beta );
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var pdf = filledarrayby( x.length, 'float64', gammaPDF );
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// Compute the CDF for each x:
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var gammaCDF = gamma.cdf.factory( alpha, beta );
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var cdf = filledarrayby( x.length, 'float64', gammaCDF );
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// Output the PDF and CDF values:
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console.log( 'x values:', x );
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console.log( 'PDF values:', pdf );
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console.log( 'CDF values:', cdf );
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// Compute statistical properties:
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var theoreticalMean = gamma.mean( alpha, beta );
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var theoreticalVariance = gamma.variance( alpha, beta );
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var theoreticalSkewness = gamma.skewness( alpha, beta );
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var theoreticalKurtosis = gamma.kurtosis( alpha, beta );
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console.log( 'Theoretical Mean:', theoreticalMean );
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console.log( 'Theoretical Variance:', theoreticalVariance );
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console.log( 'Skewness:', theoreticalSkewness );
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console.log( 'Kurtosis:', theoreticalKurtosis );
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// Generate random samples from the gamma distribution:
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var rgamma = gammaRandomFactory( alpha, beta );
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var n = 300;
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var samples = filledarrayby( n, 'float64', rgamma );
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// Compute sample mean and variance:
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var sampleMean = mean( n, samples, 1 );
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var sampleVariance = variance( n, 1, samples, 1 );
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console.log( 'Sample Mean:', sampleMean );
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console.log( 'Sample Variance:', sampleVariance );
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// Compare sample statistics to theoretical values:
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console.log( 'Difference in Mean:', abs( theoreticalMean - sampleMean ) );
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console.log( 'Difference in Variance:', abs( theoreticalVariance - sampleVariance ) );
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// Demonstrate that the sum of `k` gamma variables is a gamma-distributed sum of `k` gamma(α, β) variables with same β is `gamma(k*α, β)`:
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var k = 5;
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var sumSamples = new Float64Array( n );
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var sum;
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var i;
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var j;
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for ( i = 0; i < sumSamples.length; i++ ) {
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sum = 0.0;
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for ( j = 0; j < k; j++ ) {
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sum += rgamma();
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}
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sumSamples[ i ] = sum;
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}
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// Theoretical parameters for the sum:
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var sumAlpha = k * alpha;
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var sumMean = gamma.mean( sumAlpha, beta );
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var sumVariance = gamma.variance( sumAlpha, beta );
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console.log( 'Sum Theoretical Mean:', sumMean );
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console.log( 'Sum Theoretical Variance:', sumVariance );
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// Compute sample mean and variance for the sum:
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var sumSampleMean = mean( sumSamples.length, sumSamples, 1 );
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var sumSampleVariance = variance( sumSamples.length, 1, sumSamples, 1 );
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console.log( 'Sum Sample Mean:', sumSampleMean );
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console.log( 'Sum Sample Variance:', sumSampleVariance );
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```
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</section>

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

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Original file line numberDiff line numberDiff line change
@@ -18,7 +18,88 @@
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'use strict';
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var objectKeys = require( '@stdlib/utils/keys' );
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var gammaRandomFactory = require( '@stdlib/random/base/gamma' ).factory;
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var filledarrayby = require( '@stdlib/array/filled-by' );
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var Float64Array = require( '@stdlib/array/float64' );
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var variance = require( '@stdlib/stats/base/variance' );
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var linspace = require( '@stdlib/array/base/linspace' );
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var mean = require( '@stdlib/stats/base/mean' );
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var abs = require( '@stdlib/math/base/special/abs' );
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var gamma = require( './../lib' );
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console.log( objectKeys( gamma ) );
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// Define the shape and scale parameters:
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var alpha = 3.0; // shape parameter (α)
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var beta = 2.0; // scale parameter (β)
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// Generate an array of x values:
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var x = linspace( 0.0, 20.0, 100 );
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// Compute the PDF for each x:
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var gammaPDF = gamma.pdf.factory( alpha, beta );
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var pdf = filledarrayby( x.length, 'float64', gammaPDF );
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// Compute the CDF for each x:
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var gammaCDF = gamma.cdf.factory( alpha, beta );
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var cdf = filledarrayby( x.length, 'float64', gammaCDF );
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// Output the PDF and CDF values:
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console.log( 'x values:', x );
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console.log( 'PDF values:', pdf );
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console.log( 'CDF values:', cdf );
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// Compute statistical properties:
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var theoreticalMean = gamma.mean( alpha, beta );
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var theoreticalVariance = gamma.variance( alpha, beta );
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var theoreticalSkewness = gamma.skewness( alpha, beta );
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var theoreticalKurtosis = gamma.kurtosis( alpha, beta );
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console.log( 'Theoretical Mean:', theoreticalMean );
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console.log( 'Theoretical Variance:', theoreticalVariance );
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console.log( 'Skewness:', theoreticalSkewness );
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console.log( 'Kurtosis:', theoreticalKurtosis );
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// Generate random samples from the gamma distribution:
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var rgamma = gammaRandomFactory( alpha, beta );
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var n = 300;
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var samples = filledarrayby( n, 'float64', rgamma );
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// Compute sample mean and variance:
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var sampleMean = mean( n, samples, 1 );
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var sampleVariance = variance( n, 1, samples, 1 );
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console.log( 'Sample Mean:', sampleMean );
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console.log( 'Sample Variance:', sampleVariance );
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// Compare sample statistics to theoretical values:
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console.log( 'Difference in Mean:', abs( theoreticalMean - sampleMean ) );
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console.log( 'Difference in Variance:', abs( theoreticalVariance - sampleVariance ) );
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// Demonstrate that the sum of `k` gamma variables is a gamma-distributed sum of `k` gamma(α, β) variables with same β is `gamma(k*α, β)`:
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var k = 5;
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var sumSamples = new Float64Array( n );
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var sum;
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var i;
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var j;
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for ( i = 0; i < sumSamples.length; i++ ) {
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sum = 0.0;
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for ( j = 0; j < k; j++ ) {
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sum += rgamma();
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}
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sumSamples[ i ] = sum;
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}
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// Theoretical parameters for the sum:
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var sumAlpha = k * alpha;
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var sumMean = gamma.mean( sumAlpha, beta );
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var sumVariance = gamma.variance( sumAlpha, beta );
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console.log( 'Sum Theoretical Mean:', sumMean );
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console.log( 'Sum Theoretical Variance:', sumVariance );
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// Compute sample mean and variance for the sum:
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var sumSampleMean = mean( sumSamples.length, sumSamples, 1 );
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var sumSampleVariance = variance( sumSamples.length, 1, sumSamples, 1 );
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console.log( 'Sum Sample Mean:', sumSampleMean );
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console.log( 'Sum Sample Variance:', sumSampleVariance );

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