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docs: improve README examples of stats/base/dists/geometric namespace
PR-URL: #1801 Ref: #1628 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/geometric/README.md

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Original file line numberDiff line numberDiff line change
@@ -112,10 +112,96 @@ y = dist.logpmf( 2.3 );
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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 geometricRandomFactory = require( '@stdlib/random/base/geometric' ).factory;
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var negativeBinomial = require( '@stdlib/stats/base/dists/negative-binomial' );
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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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 geometric = require( '@stdlib/stats/base/dists/geometric' );
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console.log( objectKeys( geometric ) );
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// Define the success probability:
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var p = 0.3; // Probability of success on each trial
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// Generate an array of x values (number of failures before first success):
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var x = linspace( 0, 10, 11 ); // Geometric distribution is discrete
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// Compute the PMF for each x:
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var geometricPMF = geometric.pmf.factory( p );
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var pmf = filledarrayBy( x.length, 'float64', geometricPMF );
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// Compute the CDF for each x:
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var geometricCDF = geometric.cdf.factory( p );
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var cdf = filledarrayBy( x.length, 'float64', geometricCDF );
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// Output the PMF and CDF values:
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console.log( 'x values:', x );
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console.log( 'PMF values:', pmf );
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console.log( 'CDF values:', cdf );
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// Compute statistical properties:
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var theoreticalMean = geometric.mean( p );
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var theoreticalVariance = geometric.variance( p );
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var theoreticalSkewness = geometric.skewness( p );
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var theoreticalKurtosis = geometric.kurtosis( p );
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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 geometric distribution:
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var rgeom = geometricRandomFactory( p );
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var n = 1000;
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var samples = filledarrayBy( n, 'float64', rgeom );
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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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// Demonstrate the memoryless property:
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var s = 2.0;
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var t = 3.0;
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var prob1 = ( 1.0 - geometric.cdf( s + t - 1.0, p ) ) /
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( 1.0 - geometric.cdf( s - 1.0, p ));
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var prob2 = 1.0 - geometric.cdf( t - 1.0, p );
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console.log( 'P(X > s + t | X > s):', prob1 );
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console.log( 'P(X > t):', prob2 );
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console.log( 'Difference:', abs( prob1 - prob2 ) );
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// Demonstrate that the sum of k independent geometric random variables follows a negative binomial distribution:
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var k = 5;
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function drawSum() {
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var sum = 0;
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var j;
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for ( j = 0; j < k; j++ ) {
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sum += rgeom();
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}
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return sum;
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}
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var sumSamples = filledarrayBy( n, 'float64', drawSum );
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// Compute sample mean and variance for the sum:
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var sumSampleMean = mean( n, sumSamples, 1 );
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var sumSampleVariance = variance( n, 1, sumSamples, 1 );
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// Theoretical mean and variance of Negative Binomial distribution:
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var nbMean = negativeBinomial.mean( k, p );
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var nbVariance = negativeBinomial.variance( k, p );
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console.log( 'Sum Sample Mean:', sumSampleMean );
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console.log( 'Sum Sample Variance:', sumSampleVariance );
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console.log( 'Negative Binomial Mean:', nbMean );
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console.log( 'Negative Binomial Variance:', nbVariance );
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// Compare sample statistics to theoretical values:
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console.log( 'Difference in Mean:', abs( nbMean - sumSampleMean ) );
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console.log( 'Difference in Variance:', abs( nbVariance - sumSampleVariance ) );
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```
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</section>

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

Lines changed: 88 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -18,7 +18,93 @@
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'use strict';
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21-
var objectKeys = require( '@stdlib/utils/keys' );
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var geometricRandomFactory = require( '@stdlib/random/base/geometric' ).factory;
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var negativeBinomial = require( '@stdlib/stats/base/dists/negative-binomial' );
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var filledarrayBy = require( '@stdlib/array/filled-by' );
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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 geometric = require( './../lib' );
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console.log( objectKeys( geometric ) );
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// Define the success probability:
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var p = 0.3; // Probability of success on each trial
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// Generate an array of x values (number of failures before first success):
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var x = linspace( 0, 10, 11 ); // Geometric distribution is discrete
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// Compute the PMF for each x:
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var geometricPMF = geometric.pmf.factory( p );
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var pmf = filledarrayBy( x.length, 'float64', geometricPMF );
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// Compute the CDF for each x:
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var geometricCDF = geometric.cdf.factory( p );
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var cdf = filledarrayBy( x.length, 'float64', geometricCDF );
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// Output the PMF and CDF values:
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console.log( 'x values:', x );
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console.log( 'PMF values:', pmf );
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console.log( 'CDF values:', cdf );
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// Compute statistical properties:
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var theoreticalMean = geometric.mean( p );
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var theoreticalVariance = geometric.variance( p );
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var theoreticalSkewness = geometric.skewness( p );
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var theoreticalKurtosis = geometric.kurtosis( p );
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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 geometric distribution:
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var rgeom = geometricRandomFactory( p );
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var n = 1000;
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var samples = filledarrayBy( n, 'float64', rgeom );
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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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// Demonstrate the memoryless property:
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var s = 2.0;
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var t = 3.0;
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var prob1 = ( 1.0 - geometric.cdf( s + t - 1.0, p ) ) /
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( 1.0 - geometric.cdf( s - 1.0, p ));
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var prob2 = 1.0 - geometric.cdf( t - 1.0, p );
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79+
console.log( 'P(X > s + t | X > s):', prob1 );
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console.log( 'P(X > t):', prob2 );
81+
console.log( 'Difference:', abs( prob1 - prob2 ) );
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83+
// Demonstrate that the sum of k independent geometric random variables follows a negative binomial distribution:
84+
var k = 5;
85+
function drawSum() {
86+
var sum = 0;
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var j;
88+
for ( j = 0; j < k; j++ ) {
89+
sum += rgeom();
90+
}
91+
return sum;
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}
93+
var sumSamples = filledarrayBy( n, 'float64', drawSum );
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// Compute sample mean and variance for the sum:
96+
var sumSampleMean = mean( n, sumSamples, 1 );
97+
var sumSampleVariance = variance( n, 1, sumSamples, 1 );
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// Theoretical mean and variance of Negative Binomial distribution:
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var nbMean = negativeBinomial.mean( k, p );
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var nbVariance = negativeBinomial.variance( k, p );
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console.log( 'Sum Sample Mean:', sumSampleMean );
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console.log( 'Sum Sample Variance:', sumSampleVariance );
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console.log( 'Negative Binomial Mean:', nbMean );
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console.log( 'Negative Binomial Variance:', nbVariance );
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// Compare sample statistics to theoretical values:
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console.log( 'Difference in Mean:', abs( nbMean - sumSampleMean ) );
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console.log( 'Difference in Variance:', abs( nbVariance - sumSampleVariance ) );

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