filer/perf/simple-statistics/API.md

Basic contracts of functions:

• Functions do not modify their arguments e.g. change their order
• Invalid input, like empty lists to functions that need 1+ items to work, will cause functions to return null.

Basic Array Operations

.mixin(array)

Optionally mix in the following functions into the Array prototype. Otherwise you can use them off of the simple-statistics object itself.

If given a particular array instance as an argument, this adds the functions only to that array rather than the global Array.prototype. Without an argument, it runs on the global Array.prototype.

.mean(x)

Mean of a single-dimensional Array of numbers. Also available as .average(x)

.sum(x)

Sum of a single-dimensional Array of numbers.

.mode(x)

Returns the number that appears most frequently in a single-dimensional Array of numbers. If there are multiple modes, the one that appears last is returned.

.variance(x)

Variance of a single-dimensional Array of numbers.

.standard_deviation(x)

Standard Deviation of a single-dimensional Array of numbers.

.sample(array, n)

Return a simple random sample of the given array. The sampling is without replacement, and uses a Fisher-Yates sample to randomize.

.median_absolute_deviation(x)

The Median Absolute Deviation (MAD) is a robust measure of statistical dispersion. It is more resilient to outliers than the standard deviation. Accepts a single-dimensional array of numbers and returns a dispersion value.

Also aliased to .mad(x) for brevity.

.median(x)

Median of a single-dimensional array of numbers.

.geometric_mean(x)

Geometric mean of a single-dimensional array of positive numbers.

.harmonic_mean(x)

Harmonic mean of a single-dimensional array of positive numbers.

.root_mean_square(x)

Root mean square (RMS) of a single-dimensional array of numbers.

Also aliased to .rms(x) for brevity.

.min(x)

Finds the minimum of a single-dimensional array of numbers. This runs in linear O(n) time.

.max(x)

Finds the maximum of a single-dimensional array of numbers. This runs in linear O(n) time.

.t_test(sample, x)

Does a student's t-test of a dataset sample, represented by a single-dimensional array of numbers. x is the known value, and the result is a measure of statistical significance.

.t_test_two_sample(sample_x, sample_y, difference)

The two-sample t-test is used to compare samples from two populations or groups, confirming or denying the suspicion (null hypothesis) that the populations are the same. It returns a t-value that you can then look up to give certain judgements of confidence based on a t distribution table.

This implementation expects the samples sample_x and sample_y to be given as one-dimensional arrays of more than one number each.

.sample_variance(x)

Produces sample variance of a single-dimensional array of numbers.

.sample_covariance(a, b)

Produces sample covariance of two single-dimensional arrays of numbers.

.sample_correlation(a, b)

Produces sample correlation of two single-dimensional arrays of numbers.

.quantile(sample, p)

Does a quantile of a dataset sample, at p. For those familiary with the k/q syntax, p == k/q. sample must be a single-dimensional array of numbers. p must be a number greater than or equal to than zero and less or equal to than one, or an array of numbers following that rule. If an array is given, an array of results will be returned instead of a single number.

.chunk(sample, chunkSize)

Given a sample array, and a positive integer chunkSize, splits an array into chunks of chunkSize size and returns an array of those chunks. This does not change the input value. If the length of sample is not divisible by chunkSize, the last array will be shorter than the rest.

.shuffle(sample)

Given a sample array (with any type of contents), return a random permutation of that array, using the Fisher-Yates shuffle algorithm.

.shuffle_in_place(sample)

Given a sample array (with any type of contents), return a random permutation of that array, using the Fisher-Yates shuffle algorithm.

This changes the input array in-place, as well as returns it - unlike .shuffle(), it does not create a shallow copy of the array.

.quantile_sorted(sample, p)

Does a quantile of a dataset sample, at p. sample must be a one-dimensional sorted array of numbers, and p must be a single number from zero to one.

.iqr(sample)

Calculates the Interquartile range of a sample - the difference between the upper and lower quartiles. Useful as a measure of dispersion.

Also available as .interquartile_range(x)

.sample_skewness(sample)

Calculates the skewness of a sample, a measure of the extent to which a probability distribution of a real-valued random variable "leans" to one side of the mean. The skewness value can be positive or negative, or even undefined.

This implementation uses the Fisher-Pearson standardized moment coefficient, which means that it behaves the same as Excel, Minitab, SAS, and SPSS.

Skewness is only valid for samples of over three values.

.jenks(data, number_of_classes)

Find the Jenks Natural Breaks for a single-dimensional array of numbers as input and a desired number_of_classes. The result is a single-dimensional with class breaks, including the minimum and maximum of the input array.

.r_squared(data, function)

Find the r-squared value of a particular dataset, expressed as a two-dimensional Array of numbers, against a Function.

var r_squared = ss.r_squared([[1, 1]], function(x) { return x * 2; });

.cumulative_std_normal_probability(z)

Look up the given z value in a standard normal table to calculate the probability of a random variable appearing with a given value.

.z_score(x, mean, standard_deviation)

The standard score is the number of standard deviations an observation or datum is above or below the mean.

.standard_normal_table

A standard normal table from which to pull values of Φ (phi).

Regression

.linear_regression()

Create a new linear regression solver.

.data(1, 1], [2, 2)

Set the data of a linear regression. The input is a two-dimensional array of numbers, which are treated as coordinates, like [[x, y], [x1, y1]].

.line()

Get the linear regression line: this returns a function that you can give x values and it will return y values. Internally, this uses the m() and b() values and the classic y = mx + b equation.

var linear_regression_line = ss.linear_regression()
    .data([[0, 1], [2, 2], [3, 3]]).line();
linear_regression_line(5);

.m()

Just get the slope of the fitted regression line, the m component of the full line equation. Returns a number.

.b()

Just get the y-intercept of the fitted regression line, the b component of the line equation. Returns a number.

Classification

.bayesian()

Create a naïve bayesian classifier.

.train(item, category)

Train the classifier to classify a certain item, given as an object with keys, to be in a certain category, given as a string.

.score(item)

Get the classifications of a certain item, given as an object of category -> score mappings.

var bayes = ss.bayesian();
bayes.train({ species: 'Cat' }, 'animal');
bayes.score({ species: 'Cat' });
// { animal: 1 }