A Wren implementation of descriptive, regression, and inference statistics. Implemented in literate Wren with no dependencies. Ported from: JavaScript Simple Statistics.
import "./science/statistics" for Statistics
// Class shorthand is Ss
import "./science/statistics" for Ss- Since: 1.0.0
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: it progresses until it is close enough.
Below is an example of using epsilon in 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
var fDerivative = Fn.new { |x|
return 4 * x.pow(3) - 9 * x.pow(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 ((x_new - x_old).abs > ss.epsilon) {
x_old = x_new
x_new = x_old - stepSize * fDerivative.call(x_old)
}
// Local minimum occurs at 2.2496600165701
System.print("Local minimum occurs at %(x_new)")- Since: 1.0.0
Our default sum is the Kahan-Babuska algorithm. This method is an improvement over the classical Kahan summation algorithm. It aims at computing the sum of a list of numbers while correcting for floating-point errors. Traditionally, sums are calculated as many successive additions, each one with its own floating-point roundoff. These losses in precision add up as the number of numbers increases. This alternative algorithm is more accurate than the simple way of calculating sums by simple addition.
This runs on O(n), linear time in respect to the List.
- Example:
Ss.sum([1, 2]) // => 3- Since: 1.0.0
- Signature:
static func sum(values:List<Num>) -> Num - Parameter values: input
- Throws:
Fiber.abort()if the values are not numeric. - Returns: sum of all input numbers
The simple sum of a list is the result of adding all numbers together, starting from zero.
This runs on O(n), linear time in respect to the list
- Example:
Ss.sumsi([1, 2, 3]) // => 6- Since: 1.0.0
- Signature:
static func sumsi(values:List<Num>) -> Num - Parameter values: input
- Throws:
Fiber.abort()if the values are not numeric. - Returns: sum of all input numbers
The mean, also known as average, is the sum of all values over the number of values. This is a measure of central tendency: a method of finding a typical or central value of a set of numbers.
This runs on O(n), linear time in respect to the array
- Example:
Ss.mean([1, 2]) // => 1.5- Since: 1.0.0
- Parameter values: sample of one or more data points
- Throws:
Fiber.abort()if the the length of values is less than one - Returns: mean
The mean, also known as average, is the sum of all values over the number of values. This is a measure of central tendency: a method of finding a typical or central value of a set of numbers.
The simple mean uses the successive addition method internally to calculate it's result. Errors in floating-point addition are not accounted for, so if precision is required, the standard mean method should be used instead.
This runs on O(n), linear time in respect to the array
- Example:
Ss.mean([0, 10]) // => 5- Since: 1.0.0
- Parameter values: sample of one or more data points
- Throws:
Fiber.abort()if the the length of values is less than one - Returns: mean