Genome-wide gene insertion and deletion rates can be modelled in a maximum
likelihood framework with the additional flexibility of modelling potential missing
data using the models included within. These models simultaneously estimate insertion
and deletion (indel) rates of gene families and proportions of "missing" data for
(multiple) taxa of interest. The likelihood framework is utilized for parameter
estimation. A phylogenetic tree of the taxa and gene presence/absence patterns
(with data ordered by the tips of the tree) are required. See Dang et al.
(2016) <doi:10.1534/genetics.116.191973> for more details.

person("Chaim", "Even-Zohar", email = "chaim@ucdavis.edu", role = c("aut", "cre"))
Performs three ranking-based nonparametric tests for the
independence of two continuous variables:
(1) the classical Hoeffding's D test;
(2) a refined variant of it, named R;
(3) the Bergsma-Dassios T* sign covariance.
The first test is consistent assuming an
absolutely continuous bivariate distribution,
i.e., the population coefficient D=0
iff the variables are independent.
The latter two are consistent
under no restriction on the distribution.
All three statistics are computed
in time O(n log n) given n iid paired samples.
The computation of R and T* uses a new algorithm,
following work of Even-Zohar and Leng (2019),
see <arXiv:2010.09712>, <arXiv:1911.01414>.

Performs three ranking-based nonparametric tests for the
independence of two continuous variables:
(1) the classical Hoeffding's D test;
(2) a refined variant of it, named R;
(3) the Bergsma-Dassios T* sign covariance.
The first test is consistent assuming an
absolutely continuous bivariate distribution,
i.e., the population coefficient D=0
iff the variables are independent.
The latter two are consistent
under no restriction on the distribution.
All three statistics are computed
in time O(n log n) given n iid paired samples.
The computation of R and T* uses a new algorithm,
following work of Even-Zohar and Leng (2019),
see <arXiv:1911.01414> and references therein.