The Cauchy distribution is a special case of the t distribution when the degrees of freedom are equal to 1. The functions are related to the multivariate Cauchy distribution and include simulation, computation of the density, maximum likelihood estimation, contour plot of the bivariate Cauchy distribution, and discriminant analysis. References include: Nadarajah S. and Kotz S. (2008). "Estimation methods for the multivariate t distribution". Acta Applicandae Mathematicae, 102(1): 99--118. <doi:10.1007/s10440-008-9212-8>, and Kanti V. Mardia, John T. Kent and John M. Bibby (1979). "Multivariate analysis", ISBN:978-0124712522. Academic Press, London.

An implementation of metaheuristic algorithms for continuous optimization. Currently, the package contains the implementations of 21 algorithms, as follows: particle swarm optimization (Kennedy and Eberhart, 1995), ant lion optimizer (Mirjalili, 2015 <doi:10.1016/j.advengsoft.2015.01.010>), grey wolf optimizer (Mirjalili et al., 2014 <doi:10.1016/j.advengsoft.2013.12.007>), dragonfly algorithm (Mirjalili, 2015 <doi:10.1007/s00521-015-1920-1>), firefly algorithm (Yang, 2009 <doi:10.1007/978-3-642-04944-6_14>), genetic algorithm (Holland, 1992, ISBN:978-0262581110), grasshopper optimisation algorithm (Saremi et al., 2017 <doi:10.1016/j.advengsoft.2017.01.004>), harmony search algorithm (Mahdavi et al., 2007 <doi:10.1016/j.amc.2006.11.033>), moth flame optimizer (Mirjalili, 2015 <doi:10.1016/j.knosys.2015.07.006>, sine cosine algorithm (Mirjalili, 2016 <doi:10.1016/j.knosys.2015.12.022>), whale optimization algorithm (Mirjalili and Lewis, 2016 <doi:10.1016/j.advengsoft.2016.01.008>), clonal selection algorithm (Castro, 2002 <doi:10.1109/TEVC.2002.1011539>), differential evolution (Das & Suganthan, 2011), shuffled frog leaping (Eusuff, Landsey & Pasha, 2006), cat swarm optimization (Chu et al., 2006), artificial bee colony algorithm (Karaboga & Akay, 2009), krill-herd algorithm (Gandomi & Alavi, 2012), cuckoo search (Yang & Deb, 2009), bat algorithm (Yang, 2012), gravitational based search (Rashedi et al., 2009) and black hole optimization (Hatamlou, 2013).

This package provides a collection of statistical tests for the detection of differential item functioning (DIF) in multistage tests. Methods entail logistic regression, an adaptation of the simultaneous item bias test (SIBTEST), and various score-based tests. The presented tests provide itemwise test for DIF along categorical, ordinal or metric covariates. Methods for uniform and non-uniform DIF effects are available depending on which method is used.

This package implements the method of successive dichotomizations by Bradley and Massof (2018) <doi:10.1371/journal.pone.0206106>, which estimates item measures, person measures and ordered rating category thresholds given ordinal rating scale data.

This package provides a facility to generate various classes of fractional designs for order-of-addition experiments namely fractional order-of-additions orthogonal arrays, see Voelkel, Joseph G. (2019). "The design of order-of-addition experiments." Journal of Quality Technology 51:3, 230-241, <doi:10.1080/00224065.2019.1569958>. Provides facility to construct component orthogonal arrays, see Jian-Feng Yang, Fasheng Sun and Hongquan Xu (2020). "A Component Position Model, Analysis and Design for Order-of-Addition Experiments." Technometrics, <doi:10.1080/00401706.2020.1764394>. Supports generation of fractional designs for order-of-addition mixture experiments. Analysis of data from order-of-addition mixture experiments is also supported.

An implementation of a taxonomy of models of restricted diffusion in biological tissues parametrized by the tissue geometry (axis, diameter, density, etc.). This is primarily used in the context of diffusion magnetic resonance (MR) imaging to model the MR signal attenuation in the presence of diffusion gradients. The goal is to provide tools to simulate the MR signal attenuation predicted by these models under different experimental conditions. The package feeds a companion shiny app available at <https://midi-pastrami.apps.math.cnrs.fr> that serves as a graphical interface to the models and tools provided by the package. Models currently available are the ones in Neuman (1974) <doi:10.1063/1.1680931>, Van Gelderen et al. (1994) <doi:10.1006/jmrb.1994.1038>, Stanisz et al. (1997) <doi:10.1002/mrm.1910370115>, Soderman & Jonsson (1995) <doi:10.1006/jmra.1995.0014> and Callaghan (1995) <doi:10.1006/jmra.1995.1055>.

Fit the most popular human mortality laws', and construct full and abridge life tables given various input indices. A mortality law is a parametric function that describes the dying-out process of individuals in a population during a significant portion of their life spans. For a comprehensive review of the most important mortality laws see Tabeau (2001) <doi:10.1007/0-306-47562-6_1>. Practical functions for downloading data from various human mortality databases are provided as well.

Analyze multilevel networks as described in Lazega et al (2008) <doi:10.1016/j.socnet.2008.02.001> and in Lazega and Snijders (2016, ISBN:978-3-319-24520-1). The package was developed essentially as an extension to igraph'.

This package provides functions to perform sensitivity analysis on a model with multivariate output.

This package contains the MultiFractal Detrended Fluctuation Analysis (MFDFA), MultiFractal Detrended Cross-Correlation Analysis (MFXDFA), and the Multiscale Multifractal Analysis (MMA). The MFDFA() function proposed in this package was used in Laib et al. (<doi:10.1016/j.chaos.2018.02.024> and <doi:10.1063/1.5022737>). See references for more information. Interested users can find a parallel version of the MFDFA() function on GitHub.

Generate a stream of pseudo-random numbers generated using the MLS Junk Generator algorithm. Functions exist to generate single pseudo-random numbers as well as a vector, data frame, or matrix of pseudo-random numbers.

Translate R code into MongoDB aggregation pipelines.

This package provides methods to analyze cluster alternatives based on multi-objective optimization of cluster validation indices. For details see Kraus et al. (2011) <doi:10.1007/s00180-011-0244-6>.

The MIDASim package is a microbiome data simulator for generating realistic microbiome datasets by adapting a user-provided template. It supports the controlled introduction of experimental signals-such as shifts in taxon relative abundances, prevalence, and sample library sizes-to create distinct synthetic populations under diverse simulation scenarios. For more details, see He et al. (2024) <doi:10.1186/s40168-024-01822-z>.

Flexible, mechanistic, and spatially explicit simulator of metacommunities. It extends our previous package - rangr (see <https://github.com/ropensci/rangr>), which implemented a mechanistic virtual species simulator integrating population dynamics and dispersal. The mrangr package adds the ability to simulate multiple species interacting through an asymmetric matrix of pairwise relationships, allowing users to model all types of biotic interactions â competitive, facilitative, or neutral â within spatially explicit virtual environments. This work was supported by the National Science Centre, Poland, grant no. 2018/29/B/NZ8/00066 and the PoznaÅ Supercomputing and Networking Centre (grant no. pl0090-01).

This package provides tools for phase-type distributions including the following variants: continuous, discrete, multivariate, in-homogeneous, right-censored, and regression. Methods for functional evaluation, simulation and estimation using the expectation-maximization (EM) algorithm are provided for all models. The methods of this package are based on the following references. Asmussen, S., Nerman, O., & Olsson, M. (1996). Fitting phase-type distributions via the EM algorithm, Olsson, M. (1996). Estimation of phase-type distributions from censored data, Albrecher, H., & Bladt, M. (2019) <doi:10.1017/jpr.2019.60>, Albrecher, H., Bladt, M., & Yslas, J. (2022) <doi:10.1111/sjos.12505>, Albrecher, H., Bladt, M., Bladt, M., & Yslas, J. (2022) <doi:10.1016/j.insmatheco.2022.08.001>, Bladt, M., & Yslas, J. (2022) <doi:10.1080/03461238.2022.2097019>, Bladt, M. (2022) <doi:10.1017/asb.2021.40>, Bladt, M. (2023) <doi:10.1080/10920277.2023.2167833>, Albrecher, H., Bladt, M., & Mueller, A. (2023) <doi:10.1515/demo-2022-0153>, Bladt, M. & Yslas, J. (2023) <doi:10.1016/j.insmatheco.2023.02.008>.

This package provides tools for predicting moonlight intensity on the ground based on the position of the moon, atmospheric conditions, and other factors. Provides functions to calculate moonlight intensity and related statistics for ecological and behavioral research, offering more accurate estimates than simple moon phase calculations. The underlying model is described in Smielak (2023) <doi:10.1007/s00265-022-03287-2>.

This package provides access to well-documented medical datasets for teaching. Featuring several from the Teaching of Statistics in the Health Sciences website <https://www.causeweb.org/tshs/category/dataset/>, a few reconstructed datasets of historical significance in medical research, some reformatted and extended from existing R packages, and some data donations.

Computes regression deletion diagnostics for multivariate linear models and provides some associated diagnostic plots. The diagnostic measures include hat-values (leverages), generalized Cook's distance, and generalized squared studentized residuals. Several types of plots to detect influential observations are provided.

This package provides methods and functions to analyze the quantitative or qualitative performance for diagnostic assays, and outliers detection, reader precision and reference range are discussed. Most of the methods and algorithms refer to CLSI (Clinical & Laboratory Standards Institute) recommendations and NMPA (National Medical Products Administration) guidelines. In additional, relevant plots are constructed by ggplot2'.

This package provides a set of classes and methods to set up and run multi-species, trait based and community size spectrum ecological models, focused on the marine environment.

Multivariate Adaptive Regression Spline (MARS) based Artificial Neural Network (ANN) hybrid model is combined Machine learning hybrid approach which selects important variables using MARS and then fits ANN on the extracted important variables.

An easy-to-use IMAP client that provides tools for message searching, selective fetching of message attributes, mailbox management, attachment extraction, and several other IMAP features, paving the way for e-mail data analysis in R.

Conduct multi-locus genome-wide association study under the framework of multi-locus random-SNP-effect mixed linear model (mrMLM). First, each marker on the genome is scanned. Bonferroni correction is replaced by a less stringent selection criterion for significant test. Then, all the markers that are potentially associated with the trait are included in a multi-locus genetic model, their effects are estimated by empirical Bayes, and all the nonzero effects were further identified by likelihood ratio test for significant QTL. The program may run on a desktop or laptop computers. If marker genotypes in association mapping population are almost homozygous, these methods in this software are very effective. If there are many heterozygous marker genotypes, the IIIVmrMLM software is recommended. Wen YJ, Zhang H, Ni YL, Huang B, Zhang J, Feng JY, Wang SB, Dunwell JM, Zhang YM, Wu R (2018, <doi:10.1093/bib/bbw145>), and Li M, Zhang YW, Zhang ZC, Xiang Y, Liu MH, Zhou YH, Zuo JF, Zhang HQ, Chen Y, Zhang YM (2022, <doi:10.1016/j.molp.2022.02.012>).