## CensMixReg

 swMATH ID: 21090 Software Authors: Lachos, Víctor H.; Moreno, Edgar J.López; Chen, Kun; Cabral, Celso Rômulo Barbosa Description: Finite mixture modeling of censored data using the multivariate student-t distribution. Finite mixture models have been widely used for the modeling and analysis of data from a heterogeneous population. Moreover, data of this kind can be subject to some upper and/or lower detection limits because of the restriction of experimental apparatus. Another complication arises when measures of each population depart significantly from normality, for instance, in the presence of heavy tails or atypical observations. For such data structures, we propose a robust model for censored data based on finite mixtures of multivariate Student-$$t$$ distributions. This approach allows us to model data with great flexibility, accommodating multimodality, heavy tails and also skewness depending on the structure of the mixture components. We develop an analytically simple, yet efficient, EM-type algorithm for conducting maximum likelihood estimation of the parameters. The algorithm has closed-form expressions at the E-step that rely on formulas for the mean and variance of the multivariate truncated Student-$$t$$ distributions. Further, a general information-based method for approximating the asymptotic covariance matrix of the estimators is also presented. Results obtained from the analysis of both simulated and real datasets are reported to demonstrate the effectiveness of the proposed methodology. The proposed algorithm and methods are implemented in the new R package CensMixReg. Homepage: https://cran.r-project.org/web/packages/CensMixReg/index.html Dependencies: R Keywords: censored data; detection limit; EM-type algorithms; finite mixture models; multivariate student-t Related Software: tlmec; MomTrunc; R; lmec; AS 136; mixsmsn; QSIMVN; mclust; TTmoment; tmvtnorm; mnormt; skewlmm; EMMIXcskew; sn; CRAN; Emmixuskew; Matlab; ClusterR; trimcluster; flexmix Referenced in: 13 Publications
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### Referenced by 23 Authors

 7 Lachos Dávila, Víctor Hugo 5 Lin, Tsung I. 4 Wang, Wan-Lun 3 Cabral, Celso Rômulo Barbosa 2 Castro, Luis Mauricio 2 Dey, Dipak Kumar 2 Galarza, Christian E. 2 Jamalizadeh, Ahad 2 Matos, Larissa A. 2 Naderi, Mehrdad 1 Azzalini, Adelchi 1 Benites, Luis 1 Chen, Kun 1 Fei, Yu 1 Hung, Wenliang 1 Mirfarah, Elham 1 Morales, Christian E. Galarza 1 Moreno, Edgar J. López 1 Prates, Marcos Oliveira 1 Tian, Guoliang 1 Zeller, Camila Borelli 1 Zhai, Yibo 1 Zhang, Chi
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### Referenced in 9 Serials

 4 Journal of Multivariate Analysis 2 Computational Statistics and Data Analysis 1 Metrika 1 Computational Statistics 1 Test 1 Statistical Papers 1 Brazilian Journal of Probability and Statistics 1 Advances in Data Analysis and Classification. ADAC 1 Journal of Computational and Graphical Statistics

### Referenced in 3 Fields

 13 Statistics (62-XX) 3 Probability theory and stochastic processes (60-XX) 1 Astronomy and astrophysics (85-XX)