API Reference

API Reference

This is a guide to public-facing API (Application Programming Interface) of FSML!

Structure

The FSML procedures are categorised into several thematic modules:

FSML has five thematic modules: Basic statistics (STS), hypothesis tests (TST), linear procedures (LIN), non-linear procedures (NLP), and statistical distribution functions (DST). \label{fig:fig1}

  • STS: Basic (sample) statistics for describing and understanding data (e.g., mean, variance, correlation)
  • TST: Parametric and non-parametric hypothesis tests (e.g., Mann–Whitney U , analysis of variance)
  • LIN: Statistical procedures relying heavily on linear algebra (e.g., principal component analysis, ridge regression, linear discriminant analysis)
  • NLP: Non-linear and algorithmic procedures (e.g., k-means clustering)
  • DST: Statistical distributions (e.g., Student's t distribution); probability density function (PDF), cumulative distribution function (CDF), and percent point function (PPF)

While the public interfaces do not include these as prefixes, the handbook makes use of these categories to give it more structure. If you are interested in exploring the code, you will recognise these in module and procedure names.

Coverage

The following procedures are currently covered and have a public-facing interface. The links will take you directly to the documentation for the API.

Basic Population and Sample Statistics (STS)
Mean
Median
Variance
Standard deviation
Covariance
Linear trend
Correlation (Pearson)
Correlation (Spearman rank)


Statisical Hypothesis Tests (TST)
Student t-test (1 sample)
Paired sample t-test
Pooled t-test (2 sample)
Welch's t-test (2 sample)
Analysis of variance (one way)
Wilcoxon signed-rank (1 sample)
Wilcoxon signed-rank (paired)
Mann–Whitney U rank-sum (2 sample)
Kruskall Wallis H test


Linear Procedures (LIN)
Principal Component Analysis
Empirical Orthogonal Functions
Linear Discriminant Analysis (2-Class)
Ordinary Least Squares Regression
Ridge Regression
Mahalanobis Distance


Non-Linear Procedures (NLP)
Hierarchical Clustering
K-Means Clustering
Hybrid H/K-Means Clustering


Statistical Distribution Functions (DST)
Normal PDF
Normal CDF
Normal PPF
Student's t PDF
Student's t CDF
Student's t PPF
Gamma PDF
Gamma CDF
Gamma PPF
Exponential PDF
Exponential CDF
Exponential PPF
Chi-squared PDF
Chi-squared CDF
Chi-squared PPF
F PDF
F CDF
F PPF
Generalised Pareto PDF
Generalised Pareto CDF
Generalised Pareto PPF