# tests Martin Maechler

#### 32 packages on CRAN

Methods for Cluster analysis. Much extended the original from Peter Rousseeuw, Anja Struyf and Mia Hubert, based on Kaufman and Rousseeuw (1990) "Finding Groups in Data".

"Essential" Robust Statistics. Tools allowing to analyze data with robust methods. This includes regression methodology including model selections and multivariate statistics where we strive to cover the book "Robust Statistics, Theory and Methods" by 'Maronna, Martin and Yohai'; Wiley 2006.

Compute Hartigan's dip test statistic for unimodality / multimodality and provide a test with simulation based p-values, where the original public code has been corrected.

Maximum likelihood estimation of the parameters of a fractionally differenced ARIMA(p,d,q) model (Haslett and Raftery, Appl.Statistics, 1989).

Density, Probability and Quantile functions, and random number generation for (skew) stable distributions, using the parametrizations of Nolan.

Useful utilities ['goodies'] from Seminar fuer Statistik ETH Zurich, quite a few related to graphics; many ported from S-plus times.

Arithmetic (via S4 classes and methods) for arbitrary precision floating point numbers, including transcendental ("special") functions. To this end, Rmpfr interfaces to the LGPL'ed MPFR (Multiple Precision Floating-Point Reliable) Library which itself is based on the GMP (GNU Multiple Precision) Library.

Classes (S4) of commonly used elliptical, Archimedean, extreme value and some more copula families. Methods for density, distribution, random number generation, bivariate dependence measures, perspective and contour plots. Fitting copula models including variance estimates. Independence and serial (univariate and multivariate) independence tests, and other copula related tests. Empirical copula and multivariate CDF. Goodness-of-fit tests for copulas based on multipliers, the parametric bootstrap with several transformation options. Merged former package 'nacopula' for nested Archimedean copulas: Efficient sampling algorithms, various estimators, goodness-of-fit tests and related tools and special functions.

Onedimensional Normal Mixture Models Classes, for, e.g., density estimation or clustering algorithms research and teaching; providing the widely used Marron-Wand densities. Now fitting to data by ML (Maximum Likelihood) or EM estimation.

Datasets and Functionality from the textbook Jan Beran (1994). Statistics for Long-Memory Processes; Chapman & Hall.

Qualitatively Constrained (Regression) Smoothing Splines via Linear Programming and Sparse Matrices.

Bessel Function Computations for complex and real numbers; notably interfacing TOMS 644; approximations for large arguments, experiments, etc.

Interface to the XGobi and XGvis programs for graphical data analysis.

Simple Component Analysis (SCA) often provides much more interpretable components than Principal Components (PCA) while still representing much of the variability in the data.

Robustness -- 'eXperimental', 'eXtraneous', or 'eXtraordinary' Functionality for Robust Statistics. In other words, methods which are not yet well established, often related to methods in package 'robustbase'.

Construct directed graphs of S4 class hierarchies and visualize them. In general, these graphs typically are DAGs (directed acyclic graphs), often simple trees in practice.

Local Polynomial Regression with Ridging.

Methodology for supervised grouping aka "clustering" of potentially many predictor variables, such as genes etc.

Functions, Classes & Methods for estimation, prediction, and simulation (bootstrap) of Variable Length Markov Chain ('VLMC') Models.

Kernel density estimation with global bandwidth selection via "plug-in".

Modelling with sparse and dense 'Matrix' matrices, using modular prediction and response module classes.

Binning and plotting functions for hexagonal bins. Now uses and relies on grid graphics and formal (S4) classes and methods.

Differential Evolution (DE) stochastic algorithms for global optimization of problems with and without constraints. The aim is to curate a collection of its state-of-the-art variants that (1) do not sacrifice simplicity of design, (2) are essentially tuning-free, and (3) can be efficiently implemented directly in the R language. Currently, it only provides an implementation of the 'jDE' algorithm by Brest et al. (2006) <doi:10.1109/TEVC.2006.872133>.

Multiple Precision Arithmetic (big integers and rationals, prime number tests, matrix computation), "arithmetic without limitations" using the C library GMP (GNU Multiple Precision Arithmetic).

Several cubic spline interpolation methods of H. Akima for irregular and regular gridded data are available through this package, both for the bivariate case (irregular data: ACM 761, regular data: ACM 760) and univariate case (ACM 433 and ACM 697). Linear interpolation of irregular gridded data is also covered by reusing D. J. Renkas triangulation code which is part of Akimas Fortran code. A bilinear interpolator for regular grids was also added for comparison with the bicubic interpolator on regular grids.

A collection of functions to implement a class for univariate polynomial manipulations.

Methods for robust statistics, a state of the art in the early 2000s, notably for robust regression and robust multivariate analysis.

Routines and documentation for solving regression problems while imposing an L1 constraint on the estimates, based on the algorithm of Osborne et al. (1998)

Tools for setting up ("design"), conducting, and evaluating large-scale simulation studies with graphics and tables, including parallel computations.