**Low-Rank Methods for MVN and MVT Probabilities** (**tlrmvnmvt**)

Implementation of the classic Genz algorithm and a novel tile-low-rank algorithm for computing relatively high-dimensional multivariate normal (MVN) and Student-t (MVT) probabilities. References used for this package: Foley, James, Andries van Dam, Steven Feiner, and John Hughes. ‘Computer Graphics: Principle and Practice’. Addison-Wesley Publishing Company. Reading, Massachusetts (1987, ISBN:0-201-84840-6 1); Genz, A., ‘Numerical computation of multivariate normal probabilities,’ Journal of Computational and Graphical Statistics, 1, 141-149 (1992) <doi:10.1080/10618600.1992.10477010>; Cao, J., Genton, M. G., Keyes, D. E., & Turkiyyah, G. M. ‘Exploiting Low Rank Covariance Structures for Computing High-Dimensional Normal and Student- t Probabilities’ (2019) <https://…/2019.CGKT.manuscript.pdf>.

**Cramer von Mises Tests for Discrete or Grouped Distributions** (**cvmdisc**)

Implements Cramer-von Mises Statistics for testing fit to (1) fully specified discrete distributions as described in Choulakian, Lockhart and Stephens (1994) <doi:10.2307/3315828> (2) discrete distributions with unknown parameters that must be estimated from the sample data, see Spinelli & Stephens (1997) <doi:10.2307/3315735> and Lockhart, Spinelli and Stephens (2007) <doi:10.1002/cjs.5550350111> (3) grouped continuous distributions with Unknown Parameters, see Spinelli (2001) <doi:10.2307/3316040>. Maximum likelihood estimation (MLE) is used to estimate the parameters. The package computes the Cramer-von Mises Statistics, Anderson-Darling Statistics and the Watson-Stephens Statistics and their p-values.

**Hilbert Similarity Index for High Dimensional Data** (**hilbertSimilarity**)

Quantifying similarity between high-dimensional single cell samples is challenging, and usually requires some simplifying hypothesis to be made. By transforming the high dimensional space into a high dimensional grid, the number of cells in each sub-space of the grid is characteristic of a given sample. Using a Hilbert curve each sample can be visualized as a simple density plot, and the distance between samples can be calculated from the distribution of cells using the Jensen-Shannon distance. Bins that correspond to significant differences between samples can identified using a simple bootstrap procedure.

**Extra Binary Relational and Logical Operators** (**extraoperators**)

Speed up common tasks, particularly logical or relational comparisons and routine follow up tasks such as finding the indices and subsetting. Inspired by mathematics, where something like: 3 < x < 6 is a standard, elegant and clear way to assert that x is both greater than 3 and less than 6 (see for example <https://…/Relational_operator> ), a chaining operator is implemented. The chaining operator, %c%, allows multiple relational operations to be used in quotes on the right hand side for the same object, on the left hand side. The %e% operator allows something like set-builder notation (see for example <https://…/Set-builder_notation> ) to be used on the right hand side. All operators have built in prefixes defined for all, subset, and which to reduce the amount of code needed for common tasks, such as return those values that are true.