# Jyoti Sarkar

Professor, Department of Mathematical Sciences

## Education

- Ph.D. (1990) Statistics, University of Michigan, Ann Arbor, MI
- M. Stat. (1987) Indian Statistical Institute, Calcutta, India
- B. Stat. (1985) Indian Statistical Institute, Calcutta, India

## Research

Prof. Sarkar's major research activities are in statistical reliability theory. The general class of problems he and his collaborators study can be described as follows: "A monitored system experiences a cycle of lifetimes and repair times lasting for random 27 durations. After failure, the system undergoes a repair and is restored to operation. What is the probability that the system will be in the functioning state at any given time?" Dr. Sarkar has studied the availability of repairable systems under different models arising from the implementation of different inspection policies, different repair policies, and the presence of one or more spare units to support the main operating unit. Many other practical variations of the system availability problem remain to be solved. For example, the aspect of cost in any maintenance policy and the effect of a random environment need to be properly addressed. Dr. Sarkar is engaged in extending the frontiers of availability theory research.

Sarkar's research in statistical inference focuses on the performance of the Graybill-Deal estimator of the common mean of two populations under a two-stage or a fully sequential sampling scheme. He has also studied the optimal allocation of a fixed sampling budget in the context of estimating the common mean of a bivariate normal population when the component variables have different sampling costs. He is now working on the companion problem of optimal sampling when the objective is hypothesis testing.

Aside from his primary research areas in Statistics, Dr. Sarkar also collaborates with several economists to conduct research in location theory. They study location equilibrium for firms in various models of competition arising from different types of competition (in price or in quantity), different number of competitors (duopolists or oligopolists) and different number of stores per firm (single-store or multi-store), different types of markets (network, linear, or circular) and different entry times into the market (simultaneous or sequential).

## Publications & Professional Activities

For abstracts of papers send request to jsarkar@math.iupui.edu

##### Statistical Inference

- Lerche, H.R. and Sarkar, J. The Blackwell prediction algorithm for infinite 0-1 sequences, and a generalization, In: Statistical Decision Theory and Related Topics V, S.S. Gupta and J.O. Berger, editors, 5 (1993), 503-511, Springer-Verlag.
- De, M. and Sarkar, J. Estimation of common mean of two univariate normal populations using two stage sampling, C. S. A. Bulletin 48(189-190) (1999), 73-81.
- De, M.; Sarkar, J. and Sinha, B.K. Optimal sampling scheme for estimating the common mean of a bivariate normal population under differential sampling costs, Journal of Applied Statistical Science, 12 (2002) in press.

##### Sequential Analysis

- Sarkar, J. One-armed bandit problems with covariates, The Annals of Statistics, 199 (1991), 1978-2002.
- Boukai, B. and Sarkar, J. An accelerated bias-corrected sequential estimation for the mean of NEFPVF distributions, Sequential Analysis, 15(1) (1996), 47-60.
- Boukai, B. and Sarkar, J. Sequential confidence intervals with fixed-proportional accuracy for the mean of NEFPVF distributions, Journal of Statistical Planning and Inference, 59 (1997) 241-256.

##### Economic Location Theory

- Gupta, B., Pal, D. and Sarkar, J. Spatial Cournot competition and agglomeration in a model of location choice, Regional Science & Urban Economics, 27 (1997), 261-282.
- Sarkar, J., Gupta, B and Pal, D. Locational equilibrium for Cournot oligopoly in spatially separated markets, Journal of Regional Science, 37 (1997), 1995-212.
- Sarkar, J., Gupta, B and Pal, D. A Geometric solution of a Cournot oligopoly with non-identical firms, Journal of Economics Education, 29 (1998), 118-126.
- Pal, D. and Sarkar, J. A Stakelberg oligopoly with non-identical firms, Bulletin of Economic Research, 53(2) (2001), 127-134.
- Pal, D. and Sarkar, J. Spatial Cournot completion among multi-stored firms, International Journal of Industrial Organization, 20(2) (2002), 163-190.
- Gupta B., Pal, D. and Sarkar, J. Where to locate in a circular city? Submitted.

##### Statistical Reliability Theory

- Chaudhuri, G., Pal, N. and Sarkar, J. Estimation of the reliability function of a series system: some decision theoretic results, Statistics 32 (1998), 59-74.
- Sarkar, J. and Chaudhuri, G. Availability of a system with gamma life and exponential repair time under perfect repair policy, Statistics & Probability Letters 43 (1999), 189-1996.
- Biswas, A. and Sarkar, J. Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair, Statistics & Probability Letters, 50(2) (2000), 105-114.
- Sarkar, J. and Sarkar, S. Availability of a periodically inspected system under perfect repair. Journal of Statistical Planning and Inference, 91 (2000), 77-90.
- Sarkar, J. and Sarkar, S. Availability of a periodically inspected system supported by a spare, under perfect repair or upgrade, Statistics & Probability Letters, 53(2) (2001), 207-217.
- Biswas, A. Sarkar, J. and Sarkar, S. Availability of a periodically inspected system maintained through several imperfect repairs before a perfect repair. To appear in IEEE Transaction in Reliability.

##### Medicine

- Howard T.J., Stonerock, C.E., Sarkar, J. , Lehman, G.A., Sherman, S., Wiebke, E.A., Madura, J.A. and Broadie, T.A. Contemporary treatment strategies for external pancreatic fistulas, Surgery, 124 (1998), 627-633.
- Braun, S. and Sarkar, J. The growth of the maxilla under orthodontic treatment.

##### Enumeration

- Sarkar, J. Flipping tokens in circles, The American Mathematical Monthly, 99 (1992), 577.
- Sarkar, J. An algorithm to enumerate correlation immune Boolean functions. (in progress).
- Sarkar, J. Counting fixed-size subtrees in a regular tree. (in progress).

## Professional Affiliations

- Statistics Consulting Center
- The Institute of Mathematical Statistics, Hayward, CA (1987-)
- The American Statistical Association, Alexandria, VA (1988-), Chapter: Indianapolis, IN
- Mathematical Association of America, Washington D.C. (1990-1994)

##### Previous Positions Held

- 2000 Visiting Scholar, Indian Institute of Management, Calcutta, India
- 1999 Visiting Scientist, Statistics and Mathematics Unit, Indian Statistical Institute, Calcutta, India
- 1990 Visiting Assistant Professor, Department of Statistics,University of Michigan, Ann Arbor, MI

## Honors, Awards and Grants

- U.S. Patent 5,544,882. Puzzle including overlaying puzzle pieces. August 13, 1996.
- Teaching Excellence Recognition Award, School of Science, IUPUI. March 27, 2000.