Description: Statistical hypothesis testing methods for
non-parametric functional dependencies using asymptotic
chi-square or exact statistics. Functional chi-squares are
asymmetric and functional optimal, unique from other related
statistics. These tests reveal evidence for causality based on
the causality-by-functionality principle. They include
asymptotic functional chi-square tests, an exact functional
test, a comparative functional chi-square test, and also a
comparative chi-square test. The normalized non-constant
functional chi-square test was used by Best Performer
NMSUSongLab in HPN-DREAM (DREAM8) Breast Cancer Network
Inference Challenges. 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 dependencies not possible with
symmetrical Pearson's chi-square or Fisher's exact tests.

chi-square or exact distributions. Functional chi-squares 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

Title: Chi-Square and Exact Tests for Model-Free Functional Dependency
model-free functional dependency using asymptotic
novel means to assess directional dependency not possible with

chi-square or exact distributions. Functional
chi-squares are asymmetric and functionally optimal,
unique from other related statistics. Tests in this package
reveal evidence for causality based on the
Inference Challenges. A function index derived from the
functional chi-square offers a new effect size measure for
the strength of function 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

Title: Model-Free Functional Chi-Squared and Exact Tests
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
('Zhang & Song' 2013) <arXiv:1311.2707> and an exact
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)
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