docs: improve README examples of stats/base/dists/normal namespace

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

@@ -109,12 +109,111 @@ var y = dist.pdf( 2.0 );
 <!-- eslint no-undef: "error" -->
 
 ```javascript
-var objectKeys = require( '@stdlib/utils/keys' );
 var normal = require( '@stdlib/stats/base/dists/normal' );
 
-console.log( objectKeys( normal ) );
+/*
+A bakery is analyzing cake baking times to ensure consistency and better schedule their baking processes.
+
+The Central Limit Theorem (CLT) states that the average baking times from many batches will follow a normal distribution if there are enough batches (typically n > 30).
+
+Assuming each record represents the average baking time per batch and the bakery has collected the following data:
+
+-      Mean baking time (μ/mu): 20 minutes.
+-      Standard deviation in baking time (σ/sigma): 3 minutes.
+
+We can model the average bake times using a normal distribution with μ (mu) = 20.0 minutes and σ = 3.0 minutes.
+*/
+
+var mu = 20.0;
+var sigma = 3.0;
+
+var normalDist = new normal.Normal( mu, sigma );
+
+// Output the standard deviation of the baking times:
+console.log( normalDist.sigma );
+// => 3.0
+
+// Adjust distribution parameters
+normalDist.sigma = 4.0;
+
+// Adjusted standard deviation to reflect different variance scenario:
+console.log( normalDist.sigma );
+// => 4.0
+
+// Excess kurtosis of a normal distribution (measure of "tailedness"):
+console.log( normalDist.kurtosis );
+// => 0.0
+
+// Median baking time:
+console.log( normalDist.median );
+// => 20.0
+
+// Variance of the baking times after adjusting sigma:
+console.log( normalDist.variance );
+// => 16.0
+
+// Probability density function at the mean baking time:
+console.log( normal.pdf( 20.0, mu, sigma ) );
+// => ~0.133
+
+// Cumulative distribution function at the mean (portion of times ≤ 20 minutes):
+console.log( normal.cdf( 20.0, mu, sigma ) );
+// => ~0.5
+
+// 50th percentile (median) of the baking times:
+console.log( normal.quantile( 0.5, mu, sigma ) );
+// => 20.0
+
+// Moment-generating function value at 0.5 (used in probability theory):
+console.log( normal.mgf( 0.5, mu, sigma ) );
+// => ~67846.291
+
+// Entropy of the normal distribution (measure of uncertainty):
+console.log( normal.entropy( mu, sigma ) );
+// => ~2.518
+
+// Mean baking time:
+console.log( normal.mean( mu, sigma ) );
+// => 20.0
+
+// Median baking time:
+console.log( normal.median( mu, sigma ) );
+// => 20.0
+
+// Mode of the baking times (most frequent value):
+console.log( normal.mode( mu, sigma ) );
+// => 20.0
+
+// Variance of the baking times:
+console.log( normal.variance( mu, sigma ) );
+// => 9.0
+
+// Skewness of the distribution (symmetry measure):
+console.log( normal.skewness( mu, sigma ) );
+// => 0.0
+
+var myquantile = normal.quantile.factory( 20.0, 3.0 );
+
+// 20th percentile (value below which 20% baking times fall):
+console.log( myquantile( 0.2 ) );
+// => ~17.475
+
+// 80th percentile (value below which 80% baking times fall):
+console.log( myquantile( 0.8 ) );
+// => ~22.525
+
+var mylogpdf = normal.logpdf.factory( 20.0, 3.0 );
+
+// Logarithm of the probability density function at the mean:
+console.log( mylogpdf( 20.0 ) );
+// => ~-2.018
+
+// Logarithm of the probability density function at 15 minutes:
+console.log( mylogpdf( 15.0 ) );
+// => ~-3.406
 ```
 
+
 </section>
 
 <!-- /.examples -->

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

@@ -18,7 +18,105 @@
 
 'use strict';
 
-var objectKeys = require( '@stdlib/utils/keys' );
 var normal = require( './../lib' );
 
-console.log( objectKeys( normal ) );
+/*
+A bakery is analyzing cake baking times to ensure consistency and better schedule their baking processes.
+
+The Central Limit Theorem (CLT) states that the average baking times from many batches will follow a normal distribution if there are enough batches (typically n > 30).
+
+Assuming each record represents the average baking time per batch and the bakery has collected the following data:
+
+-      Mean baking time (μ/mu): 20 minutes.
+-      Standard deviation in baking time (σ/sigma): 3 minutes.
+
+We can model the average bake times using a normal distribution with μ (mu) = 20.0 minutes and σ = 3.0 minutes.
+*/
+
+var mu = 20.0;
+var sigma = 3.0;
+
+var normalDist = new normal.Normal( mu, sigma );
+
+// Output the standard deviation of the baking times:
+console.log( normalDist.sigma );
+// => 3.0
+
+// Adjust distribution parameters
+normalDist.sigma = 4.0;
+
+// Adjusted standard deviation to reflect different variance scenario:
+console.log( normalDist.sigma );
+// => 4.0
+
+// Excess kurtosis of a normal distribution (measure of "tailedness"):
+console.log( normalDist.kurtosis );
+// => 0.0
+
+// Median baking time:
+console.log( normalDist.median );
+// => 20.0
+
+// Variance of the baking times after adjusting sigma:
+console.log( normalDist.variance );
+// => 16.0
+
+// Probability density function at the mean baking time:
+console.log( normal.pdf( 20.0, mu, sigma ) );
+// => ~0.133
+
+// Cumulative distribution function at the mean (portion of times ≤ 20 minutes):
+console.log( normal.cdf( 20.0, mu, sigma ) );
+// => ~0.5
+
+// 50th percentile (median) of the baking times:
+console.log( normal.quantile( 0.5, mu, sigma ) );
+// => 20.0
+
+// Moment-generating function value at 0.5 (used in probability theory):
+console.log( normal.mgf( 0.5, mu, sigma ) );
+// => ~67846.291
+
+// Entropy of the normal distribution (measure of uncertainty):
+console.log( normal.entropy( mu, sigma ) );
+// => ~2.518
+
+// Mean baking time:
+console.log( normal.mean( mu, sigma ) );
+// => 20.0
+
+// Median baking time:
+console.log( normal.median( mu, sigma ) );
+// => 20.0
+
+// Mode of the baking times (most frequent value):
+console.log( normal.mode( mu, sigma ) );
+// => 20.0
+
+// Variance of the baking times:
+console.log( normal.variance( mu, sigma ) );
+// => 9.0
+
+// Skewness of the distribution (symmetry measure):
+console.log( normal.skewness( mu, sigma ) );
+// => 0.0
+
+var myquantile = normal.quantile.factory( 20.0, 3.0 );
+
+// 20th percentile (value below which 20% baking times fall):
+console.log( myquantile( 0.2 ) );
+// => ~17.475
+
+// 80th percentile (value below which 80% baking times fall):
+console.log( myquantile( 0.8 ) );
+// => ~22.525
+
+var mylogpdf = normal.logpdf.factory( 20.0, 3.0 );
+
+// Logarithm of the probability density function at the mean:
+console.log( mylogpdf( 20.0 ) );
+// => ~-2.018
+
+// Logarithm of the probability density function at 15 minutes:
+console.log( mylogpdf( 15.0 ) );
+// => ~-3.406