simple-statistics/src/epsilon.js

Simple Statistics

/**
 * We use `ε`, epsilon, as a stopping criterion when we want to iterate
 * until we're "close enough". Epsilon is a very small number: for
 * simple statistics, that number is **0.0001**
 *
 * This is used in calculations like the binomialDistribution, in which
 * the process of finding a value is [iterative](https://en.wikipedia.org/wiki/Iterative_method):
 * it progresses until it is close enough.
 *
 * Below is an example of using epsilon in [gradient descent](https://en.wikipedia.org/wiki/Gradient_descent),
 * where we're trying to find a local minimum of a function's derivative,
 * given by the `fDerivative` method.
 *
 * @example
 * // From calculation, we expect that the local minimum occurs at x=9/4
 * var x_old = 0;
 * // The algorithm starts at x=6
 * var x_new = 6;
 * var stepSize = 0.01;
 *
 * function fDerivative(x) {
 *   return 4 * Math.pow(x, 3) - 9 * Math.pow(x, 2);
 * }
 *
 * // The loop runs until the difference between the previous
 * // value and the current value is smaller than epsilon - a rough
 * // meaure of 'close enough'
 * while (Math.abs(x_new - x_old) > ss.epsilon) {
 *   x_old = x_new;
 *   x_new = x_old - stepSize * fDerivative(x_old);
 * }
 *
 * console.log('Local minimum occurs at', x_new);
 */
const epsilon = 0.0001;

export default epsilon;