Statistical hypothesis testing methods for inferring model-free functional dependency using asymptotic chi-squared or exact distributions. Functional test statistics are asymmetric and functionally optimal, unique from other related statistics. Tests in this package reveal evidence for causality based on the causality-by-functionality principle. They include asymptotic functional chi-squared tests ('Zhang & Song' 2013) <arXiv:1311.2707> and an exact functional test ('Zhong & Song' 2019) <doi:10.1109/TCBB.2018.2809743>. The normalized functional chi-squared test was used by Best Performer 'NMSUSongLab' in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges ('Hill et al' 2016) <doi:10.1038/nmeth.3773>. A function index ('Zhong & Song' in press) ('Kumar et al' 2018) <doi:10.1109/BIBM.2018.8621502> derived from the functional test statistic offers a new effect size measure for the strength of functional dependency, a better alternative to conditional entropy in many aspects. For continuous data, these tests offer an advantage over regression analysis when a parametric functional form cannot be assumed; for categorical data, they provide a novel means to assess directional dependency not possible with symmetrical Pearson's chi-squared or Fisher's exact tests.
