# Professor Jeffrey Hunter

### Professor of Mathematical Sciences

**Phone:** +64 9 921 9999 extension 5031

**Email:** jeffrey.hunter@aut.ac.nz

**Physical Address:**

AUT Tower, Level 1,

2 – 14 Wakefield St,

Auckland 1010

**Postal Address:**

School of Engineering, Computer and Mathematical Sciences

Private Bag 92006,

Auckland 1142

### Qualifications:

BSc, University of New Zealand, 1962.

MSc with First Class Honours in Mathematics, University of Auckland, 1963.

PhD in Statistics, University of North Carolina at Chapel Hill, N.C., 1968,

DSc in Applied Probability, Massey University, 2005.

### Memberships and Affiliations:

- Member of the Royal Society of New Zealand, since 1993
- New Zealand Statistical Association. Member since 1969. President 1995 - 97, Honorary Life Member 2006
- Elected Member, of the International Statistical Institute, 1993
- New Zealand Mathematical Society, Member since 1997. Elected Fellow 2002
- Member of the Operational Research Society of New Zealand, since 1969.

### Biography:

**Employment History**

Auckland University of Technology, School of Computing and Mathematical Sciences, since 2007

- Adjunct Professor in Mathematical Sciences, Aug 2007 - Feb 2009.
- Head of Research (Mathematical Sciences), Feb 2010 - present.
- Head of Mathematical Sciences, July 2010 to January 2013.
- Professor of Mathematical Sciences, July 2010 - present.

Massey University, Professor Emeritus of Statistics, 2007 -

- Institute of Information and Mathematical Sciences, Albany Campus, 1998 - 2007
- Professor and Foundation Head of Institute, 1998 – 2001,
- Professor of Statistics, 2001 - 07,
- Faculty of Information and Mathematical Sciences, 1995 - 97
- Professor and Dean of the Faculty, 1995 - 97
- Department of Statistics, Palmerston North, 1991 - 95
- Professor of Statistics and Foundation Head of the Department 1991-95
- Department of Mathematics & Statistics, Palmerston North: 1990 - 91
- Professor of Statistics, 1990 - 91

University of Auckland, Department of Mathematics and Statistics, (Dept of Mathematics until1 1982), 1969-90

- Associate Professor of Statistics, 1986 - 90
- Senior Lecturer in Statistics, 1971 - 85
- Lecturer in Statistics, 1969 - 71

### Teaching Areas:

- Applied Probability
- Stochastic Operations Research including queueing models
- Statistical theory and inference
- Probability theory

### Research Areas:

- Applied Probability focusing on Markov chains, semi-Markov processes
- Generalized matrix inverses
- Queueing theory
- Two-dimensional renewal theory.

### Publications:

**Refereed Journal Papers**

- Hunter, J.J., “Some notes on mathematical induction”, New Zealand Mathematics Magazine, 1 (2), 13 - 18, (1964)
- Hunter, J.J., “An analytical technique for urban casualty estimation from multiple nuclear weapons”, Operations Research, 16 (6), 1096 - 1108, (1967)
- Hunter, J.J., “On the renewal density matrix of a semi-Markov process”, Sankhya, The Indian Journal of Statistics, Series A, 31, 281 - 308, (1969)
- Hunter, J.J., “Two queues in parallel”, The Journal of the Royal Statistical Society, Series B, 31 (3), 432 - 445, (1969)
- Hunter, J.J., “On the moments of Markov renewal processes”, Advances in Applied Probability, 1 (2), 188 - 210, (1969)
- Hunter, J.J. “Further studies on two queues in parallel”, Australian Journal of Statistics, 13 (2), 83 - 93, (1971)
- Hunter, J.J., “Independence, conditional expectation and zero covariance”, The American Statistician, 26 (5), 22 - 24, (1972)
- Hunter, J.J., “On the occurrence of the sequence SF in Markov dependent Bernoulli trials”, Mathematical Chronicle, 2 (3), 131 - 136, (1973)
- Hunter, J.J., “Renewal theory in two dimensions, Basic results”, Advances in Applied Probability, 6 (2), 376 - 391, (1974)
- Hunter, J.J., “Renewal theory in two dimensions, Asymptotic results”, Advances in Applied Probability, 6 (3), 546 - 562, (1974)
- Hunter, J.J., “Renewal theory in two dimensions, Bounds on the renewal function”, Advances in Applied Probability, 9 (3), 527 - 541, (1977)
- Hunter, J.J., “Two queues in parallel with exponential type semi-Markovian inputs”, Opsearch, The Journal of the Operational Research Society of India, 14 (1), 29 - 37, (1977)
- Hunter, J.J., “Queueing and storage systems in parallel with correlated inputs", New Zealand Operational Research, 9 (2), 119 - 136, (1981)
- Hunter, J.J., “Generalized inverses and their applications to applied probability problems“, Linear Algebra and its Applications, 45, 157 - 198, (1982)
- Hunter, J.J., “Filtering of Markov renewal queues, I, Feedback queues”, Advances in Applied Probability, 15 (2), 349 - 375, (1983)
- Hunter, J.J., “Filtering of Markov renewal queues, II, Birth-death queues”, Advances in Applied Probability, 15 (2), 376 - 391, (1983)
- Hunter, J.J., “Filtering of Markov renewal queues, III, Semi-Markov processes embedded in feedback queues”, Advances in Applied Probability, 16 (2), 422 - 436, (1984)
- Hunter, J.J., “Filtering of Markov renewal queues, IV: Flow processes in feedback queues”, Advances in Applied Probability, 17 (2), 386 - 407, (1985)
- Hunter, J.J., “Birth-death queues with feedback”, New Zealand Operational Research, 13 (1), 39 - 49, (1985)
- Hunter, J.J., “Random triangles, order statistics and singular distributions”, International Journal of Mathematical Education in Science and Technology, 17 (2), 253 - 257, (1986)
- Hunter, J.J. and Titchener, M.R., “The synchronization process for variable length T – codes”. I.E.E. Proceedings, E, Comput. & Digital Tech., 133 (1), 54 - 64, (1986)
- Hunter, J.J., "The non - renewal nature of the quasi - input process in the M/G/1 queue", Journal of Applied Probability, 23 (3), 803 - 811, (1986)
- Hunter, J.J., "Stationary distributions of perturbed Markov chains", Linear Algebra and its Applications, 82, 201 - 214, (1986)
- Hunter, J.J., "Characterizations of generalized inverses associated with Markovian kernels", Linear Algebra and its Applications, 102, 121 - 142, (1988)
- Hunter, J.J., “Sojourn time problems in feedback queues”, QUESTA, Queueing Systems, Theory and Applications, 5, 55 - 76, (1989)
- Hunter, J.J., “Parametric forms for generalized inverses of Markovian kernels and their applications”, Linear Algebra and its Applications, 127, 71 - 84, (1990)
- Hunter, J.J., “The computation of stationary distributions of Markov chains through perturbations", Journal of Applied Mathematics and Stochastic Analysis, 4 (1), 29 - 46, (1991)
- Hunter, J.J., “A Survey of Generalized Inverses and their use in Applied Probability”, Mathematical Chronicle, 20, 13 - 26, (1991)
- Hunter, J. J., “Stationary distributions and mean first passage times in Markov chains using generalised inverses”, Asia - Pacific Journal Operational Research, 9 (2), 145 - 153, (1992)
- Hunter J. J. “Stationary distributions and mean first passage times of perturbed Markov chains”, Linear Algebra and its Applications, 410, 217 - 243, (2005)
- Hunter, J.J., “Mixing times with applications to perturbed Markov chains”, Linear Algebra and its Applications, 417, 108-123, (2006)
- Hunter, J.J., “Variance of first passage times and applications to mixing times in Markov chains”, Linear Algebra and its Applications, 429, 1135-1162, (t2008)
- Hunter, J.J., “Markovian queues with correlated arrival processes”, Asia - Pacific Journal Operational Research, 24 (4), 593-611, (2007)
- Hunter, J.J., “Simple procedures for finding mean first passage times in Markov chains”, Asia - Pacific Journal Operational Research, 24 (6), 813-829, (2007)
- Hunter, J.J., “Coupling and mixing times in a Markov chain”, Linear Algebra and its Applications, 430, 2607-2621, (2009)
- Hunter, J.J., “Some stochastic properties of semi-magic and magic Markov chains”. Linear Algebra and its Applications, 433, 893-907, (2010)
- Hunter, J. J., “Markov chain properties in terms of column sums of the transition matrix”, Acta et Commentationes Universitatis Tartuensis de Mathematica. Volume 16 (1), 33 - 51, (2012)
- Hunter, J. J., "The Distribution of Mixing Times in Markov Chains". Asia-Pacific Journal of Operational Research. Volume 30(1), 1250045, 1 - 29, (2013)
- Hunter, J. J., "The role of Kemeny's constant in properties of Markov Chains" Communications in Statistics - Theory and Methods, 43: 1 - 13, (2014).
- Hunter, J.J., “Generalized inverses of Markovian kernels in terms of properties of the Markov chain”, Linear Algebra and its Applications, 447, 38-55 (2014).
- Hunter J.J., “Shayle R Searle: Pioneer in Linear Modelling", Australia and New Zealand Journal of Statistics, 57 (1) 1-14 (2015).
- Hunter J.J., ”Accurate calculations of Stationary Distributions and Mean First Passage Times in Markov Renewal Processes and Markov Chains”. Special Matrices 4:151-175 (2016).
- Gustafson K. & Hunter J.J. “Why the Kemeny Time is a Constant” Special Matrices 4:176-180 (2016).

**Books**

- Hunter, J.J., “Mathematical Techniques of Applied Probability, Volume 1, Discrete Time Models: Basic Theory”. Academic Press, New York, N.Y. (Operations Research and Industrial Engineering Series) pp. xiii + 239, (ISBN: 0-12-361801-0 (v. 1), (1983). Republished as “Mathematical Techniques of Applied Probability, 1st Edition, Discrete Time Models: Basic Theory” as an e-Book, Elsevier Science (2014).
- Hunter, J.J., “Mathematical Techniques of Applied Probability, Volume 2, Discrete Time Models: Techniques and Applications”. Academic Press, New York, N.Y. (Operations Research and Industrial Engineering Series) pp. xiii + 286, (ISBN: 0-12-361802-9 (v. 2), (1983)

**Book Chapters:**

- Hunter, J.J.: "Queues and Simulation", Mathematics Form 7 Teachers Guide, Mathematics with Statistics: Supplement, Department of Education, New Zealand, 3.90 - 3.96, (1988)
- Hunter, J.J., “Mathematical Techniques for Warranty Analysis”, Chapter 7, (pp157-190), Product Warranty Handbook, An Integrated Approach to the Analysis of Warranty Policies, W.R. Blischke and D.N.P. Murthy, Editors, Marcel Dekker, ISBN: 0-8247-8955-5, (1996)
- Hunter, J.J., “New Zealand Statistical Association” Encyclopedia of Statistical Sciences, Update Volume 3, (p536), S. Kotz, Editor, John Wiley and Sons, New York, ISBN: 0-471-23883-X, (1999)
- Hunter, J.J., “A Survey of Generalized Inverses and their use in Stochastic Modelling”, (pp79-90), Advances in Probability and Stochastic Processes, A Volume in Honor of Professors R.P. Pakshirajan, G. Sankaranarayanan & S.K. Srinivasan, A. Krishnamoorthy, N. Raju and V. Ramaswami (Editors), Notable Publications Inc., New Jersey, USA. ISBN: 0-9665847-2-4, (2001)
- Hunter, J.J., “Bounds on Expected Coupling Times in a Markov Chain”, (pp271-294), “Statistical Inference, Econometric Analysis and Matrix Algebra. Festschrift in Honour of Götz Trenkler”, Bernhard Schipp and Walter Krämer (Editors), Physica-Verlag Heidelberg. ISBN: 978-3-7908-2120-8 e-ISBN: 978-3-7908-2121-5 (2009)
- Hunter J. J., “The Derivation of Markov Chain Properties using Generalized Matrix Inverses” (pp 61-89) “Lectures on Matrix and Graph Methods” Ravindra B. Bapat, Steve Kirkland, K. Manjunatha Prasad and Simo Puntanen (Editors), Manipal University Press, Manipal, Karnataka, India. ISBN: 978-81-922759-6-3 (2012)

** **

**Refereed paper in conference/meeting/symposia proceedings**

- Hunter, J.J., “Queue length processes, from different viewpoints“, New Zealand Operational Research, Proceedings of the 17th Annual Conference ORSNZ, 33 - 40, (1981)
- Hunter, J.J., “Flow processes in Birth-Death Feedback Queues”, Proceedings of the Pacific Statistical Congress, 1985, I.S. Francis, B.F.J. Manly and F.C. Lam (Editors), Elsevier Science (Amsterdam), 195 - 197, (1986)
- Hunter, J.J., “Sojourn time problems in feedback queues”, Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems, Ithaca, New York, United States, ISSN:0257-0130, J. C. Baltzer AG, Science Publishers, Red Bank, NJ, USA, 55-76, (1989)
- Hunter, J. J. (2006). Perturbed Markov Chains. In Peter Brown, Shuangzhe Liu and Dharmendra Sharma (Eds.), Contributions to Probability and Statistics - Applications and Challenges: Proceedings of the International Statistics Workshop, University of Canberra, 4-5 April 2005, (pp 99-112). World Scientific, Singapore. ISBN 981-270-391-8

**Editorials**

- Hunter J.J., Puntanen S., Styan G.P.H., Preface to the Fourth Special Issue on Matrices and Statistics, Linear Algebra and its Applications, 210, 1-2 (1994)
- Hunter, J.J., Styan G.P.H., “Foreword”, Research Letters in the Information & Mathematical Sciences, Volume 8, iii - v, Special Issue: Proceedings of the 14th International Workshop on Matrices and Statistics, July 2005.
- Ahmed S.E., Hunter J.J., Styan G.P.H., Trenkler G,. Preface to the Proceedings of the 16th International Workshop on Matrices and Statistics, Windsor 2007, Linear Algebra and its Applications, 430, 2563-2565 (2009)

### Awards:

**Prominent Service Achievements**

During his career Professor Hunter has held visiting positions at the Department of Statistics, University of North Carolina at Chapel Hill, (1973, 1988, 2001), Department of Industrial Engineering and Operations Research, Virginia Polytechnic Institute and State University, Blacksburg, (College of Engineering Visiting Professor 1980, 1987) and has been an academic visitor at the Department of Mathematics and Statistics, McGill University, Montreal, (1988), Mathematical Sciences Institute, Cornell University (1988), Statistical Laboratory, University of Cambridge, U.K (1992), Department of Industrial Engineering, Texas A & M University (1992) and Department of Statistics, University of Oxford, U.K., (2002).

In 1992 he was awarded a Claude McCarthy Fellowship to visit universities in the U.S., Canada, United Kingdom and South Africa.

In 1992 he was the Distinguished Lecturer in Applied Probability, Department of Industrial Engineering, Texas A & M University.

Served as Chair of the Royal Society of New Zealand Committee on Mathematical and Information Sciences (1997 – 2002). For his services to the Mathematical Sciences he was awarded a Bronze New Zealand Science & Technology Medal in 2003. In 2006 he was the recipient of the Campbell Award, the highest award given by the New Zealand Statistical Association, “to recognize his contributions to statistical research and education, and his services to the profession of statistics“.

Appointed to the Advisory Board of Christ’s University in Pacific, Nuku’alofa, Tonga in 2015.

Last updated: 13-Apr-2016 1.23pm

The information on this page was correct at time of publication. For a comprehensive overview of AUT qualifications, please refer to the Academic Calendar.