docs: improve examples of stats/base/dists/exponential namespace

PR-URL: #2688 
Closes: #1624

---------

Co-authored-by: Philipp Burckhardt <[email protected]>
Reviewed-by: Philipp Burckhardt <[email protected]>

Author: UtkershBasnet

lib/node_modules/@stdlib/stats/base/dists/exponential/README.md

@@ -109,10 +109,51 @@ var y = dist.logpdf( 0.8 );
 <!-- eslint no-undef: "error" -->
 
 ```javascript
-var objectKeys = require( '@stdlib/utils/keys' );
+var Float64Array = require( '@stdlib/array/float64' );
+var randomExponential = require( '@stdlib/random/array/exponential' );
+var dcusum = require( '@stdlib/blas/ext/base/dcusum' );
 var exponential = require( '@stdlib/stats/base/dists/exponential' );
 
-console.log( objectKeys( exponential ) );
+// Simulate interarrival times of customers entering a store:
+var lambda = 0.5; // Average rate (customers per minute)
+var numCustomers = 10;
+
+// Generate interarrival times using the exponential distribution:
+var interarrivalTimes = randomExponential( numCustomers, lambda, {
+    'dtype': 'float64'
+});
+
+console.log( 'Simulated interarrival times for ' + numCustomers + ' customers:' );
+console.log( interarrivalTimes );
+
+// Calculate cumulative arrival times by computing the cumulative sum of interarrival times:
+var arrivalTimes = new Float64Array( interarrivalTimes.length );
+dcusum( interarrivalTimes.length, 0.0, interarrivalTimes, 1, arrivalTimes, 1 );
+
+console.log( '\nCustomer arrival times:' );
+console.log( arrivalTimes );
+
+// Probability that a customer arrives within two minutes:
+var x = 2.0;
+var prob = exponential.cdf( x, lambda );
+console.log( '\nProbability that a customer arrives within ' + x + ' minutes: ' + prob.toFixed(4) );
+
+// Expected time until the next customer arrives:
+var mean = exponential.mean( lambda );
+console.log( 'Expected interarrival time: ' + mean + ' minutes' );
+
+var dist = new exponential.Exponential( lambda );
+
+var median = dist.median;
+console.log( 'Median interarrival time: ' + median + ' minutes' );
+
+// Evaluate the PDF at x = 1.0:
+var out = dist.pdf( 1.0 );
+console.log( 'PDF at x = 1: ' + out.toFixed(4) );
+
+// Evaluate the MGF at t = 0.1:
+out = dist.mgf( 0.1 );
+console.log( 'MGF at t = 0.5: ' + out.toFixed(4) );
 ```
 
 </section>

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

@@ -18,7 +18,48 @@
 
 'use strict';
 
-var objectKeys = require( '@stdlib/utils/keys' );
+var Float64Array = require( '@stdlib/array/float64' );
+var randomExponential = require( '@stdlib/random/array/exponential' );
+var dcusum = require( '@stdlib/blas/ext/base/dcusum' );
 var exponential = require( './../lib' );
 
-console.log( objectKeys( exponential ) );
+// Simulate interarrival times of customers entering a store:
+var lambda = 0.5; // Average rate (customers per minute)
+var numCustomers = 10;
+
+// Generate interarrival times using the exponential distribution:
+var interarrivalTimes = randomExponential( numCustomers, lambda, {
+	'dtype': 'float64'
+});
+
+console.log( 'Simulated interarrival times for ' + numCustomers + ' customers:' );
+console.log( interarrivalTimes );
+
+// Calculate cumulative arrival times by computing the cumulative sum of interarrival times:
+var arrivalTimes = new Float64Array( interarrivalTimes.length );
+dcusum( interarrivalTimes.length, 0.0, interarrivalTimes, 1, arrivalTimes, 1 );
+
+console.log( '\nCustomer arrival times:' );
+console.log( arrivalTimes );
+
+// Probability that a customer arrives within two minutes:
+var x = 2.0;
+var prob = exponential.cdf( x, lambda );
+console.log( '\nProbability that a customer arrives within ' + x + ' minutes: ' + prob.toFixed(4) );
+
+// Expected time until the next customer arrives:
+var mean = exponential.mean( lambda );
+console.log( 'Expected interarrival time: ' + mean + ' minutes' );
+
+var dist = new exponential.Exponential( lambda );
+
+var median = dist.median;
+console.log( 'Median interarrival time: ' + median + ' minutes' );
+
+// Evaluate the PDF at x = 1.0:
+var out = dist.pdf( 1.0 );
+console.log( 'PDF at x = 1: ' + out.toFixed(4) );
+
+// Evaluate the MGF at t = 0.1:
+out = dist.mgf( 0.1 );
+console.log( 'MGF at t = 0.5: ' + out.toFixed(4) );