Prof Andriëtte Bekker

Tel: 012 420 2523

Email: [email protected]

Position: Extra-ordinary Professor 

Focus Area Coordinator: Statistical Theory and Applied Statistics (see link), Centre of Excellence in Mathematical and Statistical Sciences, University of the Witwatersrand

Current NRF Rating: C1

Academic qualifications: BSc, BSc Hons, HDE, MSc (UJ), PhD (UNISA)

Research interests:

statistical distribution theory, Bayesian statistics and theory, matrix variate distributions, multivariate analysis

Current subjects to be lectured:

MVA 710, MVA 720 (multivariate analysis)

 

Current postgraduate students:

PhD: P Nagar, C Geldenhuys, M Wagener, J Smith

Various masters and honours students currently under my supervision

Previous postgraduate students:

PhD (past 8 years): R Ehlers, K Adamski, J Kleyn, J van Niekerk, MT Loots, JT Ferreira, S Makgai

Various masters and honours students successfully completed

 

Awards and scientific/scholarly recognition:

  • Elected member of the International Statistical Institute (ISI)
  • 2001-2006: NRF L rating
  • From 2007: NRF C2 rating.
  • From 2019: NRF C1 rating

 

Associate Editor:

  • Communications in Statistics-Theory and Methods (LSTA)/Simulation and Computation (LSSP).
  • Mathematical Problems in Engineering
  • Journal of Iranian Statistical Society
  • Guest editor for the STATISTICS, OPTIMIZATION AND INFORMATION COMPUTING journal for the Special Issue on Computational Techniques in Theoretical and Applied Statistics, Vol. 6, September 2018.
  • Guest editor for MATHEMATICAL PROBLEMS IN ENGINEERING Special Issue on Recent Trends in Statistical Methodologies within Communications and Systems Engineering, October 2019.
  • Editor of Springer Book “Computational and Methodological Statistics and Biostatistics: Contemporary Essays in Advancement”, 2020.

 

Recent publications (past 8 years):

BEKKER, A.  ROUX, J.J.J. & EHLERS, R. & ARASHI, M. (2011). The bimatrix variate beta type IV distribution: relation to Wilks’s statistic and bimatrix variate Kummer-beta type IV distribution. Communications in Statistics-Theory and Methods, 40, (23), 4165-4178.

BEKKER, A.  ROUX, J.J.J. & ARASHI, M. (2011). Exact nonnull distribution of Wilks’s Statistic: ratio and product of independent components.  Journal of Multivariate Analysis, 102, 619-628. (http://dx.doi.org/10.1016/j.jmva.2010.11.005)

BODVIN, L., BEKKER, A. & ROUX, J.J.J. (2011). Shannon Entropy as a Measure of Certainty in a Bayesian Calibration Framework with Bivariate Beta Priors. South African Statistical Journal, 45(2), 171-204.

BEKKER, A.  ROUX, J.J.J. & ARASHI, M. (2011). Wishart ratios with dependent structure: new members of the bimatrix beta type IV. Linear Algebra and its Applications, 435, 3243–3260.

JACOBS, R., BEKKER, A. & HUMAN, S.W., (2011) ‘n Nuwe ontwikkeling tot die bivariate betaveld, Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 30(1), Art.#103, 2 pages. doi: http://dx.doi.org/10.4102/satnt.v30i1.103.

ADAMKSI, K. HUMAN, S.H. & BEKKER, A. (2012). A generalized multivariate beta distribution: control charting when the measurements are from an exponential distribution. Statistical Papers, Volume 53, Issue 4 , 1045-1064. 

JACOBS, R., BEKKER, A.  & HUMAN, S.W. (2012). On the bivariate Kummer-beta type IV distribution. Communications in Statistics-Theory and Methods, 41, 3339-3354.

EHLERS, R., BEKKER, A. & ROUX, J.J.J. (2012). Triply noncentral bivariate beta type V distribution. South African Statist. J. 46, 221–246.

BEKKER, A.  ROUX, J.J.J., EHLERS, R. & ARASHI, M. (2012). Distribution of the product of determinants of noncentral bimatrix beta variates. Journal of Multivariate Analysis, 109, 73-87. http://dx.doi.org/10.1016/j.jmva.2012.02.016

VAN NIEKERK, J. & BEKKER, A. (2012). Bayesian estimators of the location parameter of the normal distribution with unknown variance. Peer-reviewed Proceedings of SASA 2012, p 10-17.

ADAMSKI, K., HUMAN, S.W. A BEKKER, A. & ROUX, J.J.J. (2013). Noncentral generalized multivariate beta type II distribution. RevStat-Statistical Journal, 11, 1, p 17-43.

VAN DEN BERG, J., ROUX, J.J.J. & BEKKER, A.  (2013). On a generalisation of Jensen's bivariate gamma distribution. Communications in Statistics-Theory and Methods. 42(9), 3514–3527.

LOOTS, M.T., BEKKER, A. ARASHI, M. & ROUX, J.J.J. (2013). On the real representation of quaternion variables. Statistics, 47(6), 1224-1240.

NAKALE, S., COETSEE,J., ARASHI, M. & BEKKER,A. (2013). Feasible generalised least squares estimators in serially correlated error models from an asymmetry viewpoint. Peer-reviewed Proceedings of SASA 2013, 53-60.

FERREIRA, J.T. & BEKKER, A. (2014). Objektiewe beramers vir die gesensoreerde Rayleigh-model onder verskillende verliesfunksie. Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 33(1), Art. #1040, 2 pages. http://dx.doi.org/10.4102/satnt.v33i1.1040

COETSEE, J., BEKKER, A.  & MILLARD, S. (2014). Preliminary-test and Bayes Estimation of a Location Parameter Under Blinex Loss.  Communications in Statistics-Theory and Methods, 43, 3641-3660.

ARASHI, M. BEKKER, A., ROUX, J.J.J. & RATNAPARKHI, M. (2014). A New Definition of Form-Invariance Matrix Variate Distributions. South African Statist. J., 48, 205 – 212.

ARASHI, M., BEKKER, A.  & LOOTS, M.T. & ROUX, J.J.J. (2015). Integral representation of quaternion elliptical density and its applications. Communications in Statistics-Theory and Methods, 44,4,778-789. DOI:10.1080/03610926.2012.753089

NAKALE, S., KLEYN, J., ARASHI, M. & BEKKER, A. (2015). The performance of serial correlation preliminary test estimators under asymmetry loss functions. South African Statistical Journal, 49, 121-138.

VAN NIEKERK, J., BEKKER, A., ARASHI, M. & ROUX, J.J.J. (2015) Subjective Bayesian analysis on elliptical contoured model. Communications in Statistics-Theory and Methods, 44(17), 3738-3753.

JACOBS, R., BEKKER, A., VAN DER VOET, H & TER BRAAK, C. (2015). Parametric estimation of P(X > Y) for normal distributions in the context of probabilistic environmental risk assessment. PeerJ 3:e1164; DOI 10.7717/peerj.1164.

FERREIRA, J. BEKKER, A. & ARASHI, M. (2016). Objective Bayesian estimators for the right censored Rayleigh distribution: evaluating the Al-Bayatti loss function. RevStat-Statistical Journal, 14(4) 433-454.

FERREIRA, J. BEKKER, A & ARASHI, M. (2016). Bivariate noncentral distributions: an approach via the compounding method. South African Statistical Journal, 50(1), 103-122.

VAN NIEKERK, J., BEKKER, A., ARASHI, M. & DE WAAL, D.J. (2016). Matrix variate elliptical model- subjective Bayesian inference. South African Statistical Journal, 50(1) 149-170.

MOSTERT P.J., BEKKER A. & ROUX J.J.J. (2016). A Bayesian analysis of the censored Rayleigh model when using a generalised hypergeometric as a prior. South African Statistical Journal, 50(2), 195-219.

MAKGAI, S., BEKKER, A., FERREIRA, J.T. & ARASHI, M. (2017). New results from a beta-Pareto class. South African Statistical Journal, 51, 345-360.

VAN NIEKERK, J., BEKKER, A & ARASHI, M. (2017). A gamma-mixture class of distributions with Bayesian application. Communications in Statistics- Simulation and Computation,  (46) 10, 8152-8165, http://dx.doi.org/10.1080/03610918.2016.1267754

BEKKER, A., VAN NIEKERK, J & ARASHI, M. (2017). Wishart distributions: Advances in theory with Bayesian application. Journal of Multivariate Analysis. 155,  272–283  http://dx.doi.org/10.1016/j.jmva.2016.12.002

KLEYN, J., ARASHI, M., BEKKER, A. & MILLARD, S. (2017). Preliminary Testing of the Cobb-Douglas Production Function and Related Inferential Issues Communications in Statistics- Simulation and Computation. 46(1) 469-488. http://dx.doi.org/10.1080/03610918.2014.968724.

ARASHI, M., BEKKER, A. & VAN NIEKERK, J. (2017). The weighted-type Wishart distributions with application. RevStat-Statistical Journal, 15(1), 205-222.

FERREIRA, J. BEKKER, A &  ARASHI, M. Advances in Wishart-type modelling of channel capacity Accepted in 2017 to appear in RevStat-Statistical Journal.

BEKKER, A. and FERREIRA, J.T. 2018. Bivariate gamma type distributions for modeling wireless performance metrics. Statistics, Optimization and Information Computing, 6, 335–353.

BEKKER, A., M. ARASHI, M, & FERREIRA, J.T. (2019). New bivariate gamma types with MIMO application. Communications in Statistics-Theory and Methods, 48:3, 596-615.

MARQUES, F, LOOTS, M.T. & BEKKER, A. (2019). Series representations for density functions of a family of distributions - application to the sum of independent Rayleigh random variables. Math Meth Appl Sci. 2019; 1–18.

ARASHI, M. BEKKER, A. & VAN NIEKERK, J. (2019). Weighted Distributions of Eigenvalues. Linear Algebra and its Applications, 561,1-17.

BEKKER, A, ARASHI, A. & FERREIRA, J.T. ROWLAND, B, (2018). Computational methods applied to a skewed generalised normal family. Communications in Statistics - Simulation and Computation. https://doi.org/10.1080/03610918.2018.1530785

VAN NIEKERK, J, BEKKER, A. &  ARASHI, M. (2018). Beta regression in the Presence of Outliers- A wieldy Bayesian solution. Accepted in Statistical Methods in Medical Research. DOI: 10.1177/0962280218814574

BILANKULU, V., BEKKER, A. & MARQUES, F.J. (2018). The Ratio of Independent Generalized Gamma Random Variables with Applications. Accepted to Computational and Mathematical Methods.

FERREIRA, J.T.  and BEKKER, A. (2019). A unified complex noncentral Wishart type distribution inspired by massive MIMO systems. Journal of Statistical Distributions and Applications, 6(4),1-19.

BEKKER, A., NAGAR, P., ARASHI, M & RAUTENBACH. H. 2019. From Symmetry to Asymmetry on the Disc Manifold: Modelling of Marion Island Data. Symmetry, 11 (8) p1030-1030. DOI: 10.3390/sym11081030.

NADERI, M., HASHEMI, F., BEKKER, A. & JAMALIZADEH A. (2020). Modelling right-skewed financial data stream with outliers: a Likelihood-based inference via finite mixture of the generalized Birnbaum-Saunders distributions. Applied Mathematics and Computation. 376: 125109

FERREIRA, J.T., BEKKER, A., MARQUES, F. & LAIDLAW, M  (2020). An Enriched α-µ model as fading candidate. Invited paper for the special issue “Recent trends in statistical methodologies within communications- and systems engineering”,  Mathematical Methods in Engineering,  Article ID 5879413, https://doi.org/10.1155/2020/5879413

ARASHI, M., NAGAR, P. AND BEKKER, .A.(2020). Joint probabilistic modelling of wind speed and wind direction for wind energy analysis: a case study in Humansdorp and Noupoort. Sustainability,12(11), 4371; https://doi.org/10.3390/su12114371

NADERI, M. BEKKER, A., ARASHI, M. & JAMALIZADEH, A. (2020). A theoretical framework for Landsat data modeling based on the matrix variate mean-mixture of normal model. PLOS ONE, https://doi.org/10.1371/journal.pone.0230773.

ROOZEGAR, R. , BALAKRISHNAN, N., BEKKER, A AND  JAMALIZADEH, A. 2020. On multivariate selection of scale mixtures of normal distributions. Brazilian Journal of Probability and Statistics. 35 (2), 351-374.

NEETHLING, A FERREIRA, JT BEKKER A AND NADERI M. (2020). Skew generalised normal innovations for the AR(p) model. Symmetry. 12, 1253; https://doi.org/10.3390/sym12081253

VAN NIEKERK, J, BEKKER, A. AND ARASHI, M. (2021). Matrix-variate beta generators - developments and application. Accepted for Special issue of Journal of the Iranian Statistical  Society- Behboodian Memorial issue.

VISAGIE,I.J.H., DE WAAL, D., MAKGAI,S. AND  BEKKER, A. (2021). Contributions to the class of beta-generated distributions, accepted to Communications in Statistics-Theory and Methods.

BOTHA, T, FERREIRA, JT & BEKKER, A (2021). Alternative Dirichlet Priors for Estimating Entropy via a Power Sum Functional, Mathematics, 9, 1493. https://doi.org/10.3390/math9131493

HASHEMI, F, BEKKER, A, SMITH, K & ARASHI, M (2021). Sibling rivalry within inverse Weibull family to predict the COVID-19 spread in South Africa. Communications in Statistics-Case studies and Data Analysis, https://doi.org/10.1080/23737484.2021.1979433

BEKKER, A, HASHEMI, F & ARASHI, M (2021). Flexible factor model for handling missing data in supervised learning. Accepted in Communications in Mathematics and Statistics.

MAKGAI, SL, BEKKER, A & ARASHI, M (2021). Compositional data modelling through Dirichlet innovations Mathematics, 9, 2477. https://doi.org/10.3390/math9192477 

NAGAR, P, BEKKER, A & ARASHI, M (2021). Mean mixtures in directional statistics. Proceedings of 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems.

RAD,NN,  BEKKER, A &  ARASHI, M (2021). Bayesian inference for skew-wrapped Cauchy mixture model using a modified Gibbs sampler. Proceedings of 2021 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems.

WAGENER, M, BEKKER, A & ARASHI, M (2021). Mastering the body and tail shape of a distribution.  Mathematics,  9, 2648. https://doi.org/10.3390/math9212648

ARASHI, M, RAD, NN, BEKKER, A & SCHUBERT, WD (2021). Möbius transformation-induced distributions provide better modelling for protein architecture. Mathematics, 9, (21), 2749; https://doi.org/10.3390/math9212749.

ARASHI, A.  BEKKER, A, SALEHI M, MILLARD S, CRONJE T, & GOLPAYGANI, M (2021). Evaluating prediction of COVID-19 at provincial level of South Africa; a statistical perspective Accepted Environmental Science and Pollution Research.

FERREIRA, J.T., BEKKER, A., BOTHA, C. & MAKGAI, S. (2021). A note on the probabilistic determinant of independent generalized beta entries. Accepted Proceedings, SASA 2021.

SMITH, J, ARASHI, M & BEKKER, A (2022). Empowering Differential Networks Using Bayesian Analysis. Accepted Plos One.

BEKKER , A., FERREIRA, J.T., HUMAN, S.W. & ADAMSKI, K. (2022). Capturing a Change in the Covariance Structure of a Multivariate Process, Accepted in Symmetry. 

ARASHI, M , RAD, NN, BEKKER, A  &  LEY, C (2022). A Coming Together of Bayesian Inference and Skew Spherical Data. Invited: Accepted in Frontiers in BIG DATA.

 

 

Book chapters

MARQUES, F.J., GHOSH, I., FERREIRA, J.T., AND BEKKER, A. “A note on the product of independent beta random variables”. Accepted. Emerging Topics in Statistics and Biostatistics, Springer.( Book chapter honoring Prof. Barry C Arnold's 80th birthday) 2021, Advances in Statistics - Theory and Applications. https://www.springer.com/gp/book/9783030628994

 

BEKKER, A. RAD, N.N. ARASHI, M AND LEY, C. (2021). Generalized Skew-Symmetric Circular and Toroidal Distributions. Directional Statistics for Innovative Applications" International in commemoration of the Bicentennial birth anniversary of Lady Florence Nightingale, O.M. Springer , editors Ashis SenGupta  and  Barry C. Arnold. 2021.  

 

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