Program                                                          Institution/University                                   Year of completion

Ph.D.                                                                  IIT Madras                                                                        2018

M.Sc. Mathematics                                     IIT Madras                                                                        2013

B.Sc (Hons) Mathematics                        University of Delhi                                                        2010

Subject                      : Mathematics

Area of research   : Applied Probability

Ph.D. Supervisor : Dr. Neelesh S. Upadhye 

Specializations    : (a) Stein's method for distributional approximation

                                       (b) Distribution theory of runs and patterns

1. Kumar, A. N. and Vellaisamy, P., Binomial approximation to locally dependent collateralized debt obligations, Methodol. Comput. Appl. Probab., (2023) (accepted). https://arxiv.org/abs/2203.12895 

2. Kumar, A. N., Bounds on negative binomial approximation to call function, Revstat Stat. J., (2022) (accepted). https://revstat.ine.pt/index.php/REVSTAT/article/view/437  

3. Kumar, A. N., Upadhye, N. S., and Vellaisamy P., Approximations related to sum of m-dependent random variables, Braz. J. Probab. Stat., 36(2), 349-368, 2022. https://doi.org/10.1214/21-BJPS529 

4. Kumar, A. N., Vellaisamy, P., and Viens, F., Poisson approximation to the convolution of power series distributions, Probab. Math. Statist., 42(1), 63-80, 2022. https://doi.org/10.37190/0208-4147.00056 

5. Kumar, A. N. and Upadhye, N. S., On discrete Gibbs measure approximation to runs, Comm. Statist. Theory Methods, 51(5), 1488-1513, 2022. https://doi.org/10.1080/03610926.2020.1765256 

6. Kumar, A. N., Approximations to the weighted sums of random variables, Bull. Malaysian Math. Sci. Soc., 44(4), 2447–2464 2021. https://doi.org/10.1007/s40840-021-01077-z 

7. Kumar, A. N. and Upadhye, N. S., Generalizations of distributions related to (k1, k2)-runs, Metrika, 82(2), 249-268, 2019. https://doi.org/10.1007/s00184-018-0668-x 

8. Upadhye, N. S. and Kumar, A. N., Pseudo-binomial approximation to (k1, k2)-runs, Statist. Probab. Lett., 141, 19-30, 2018. https://doi.org/10.1016/j.spl.2018.05.016 

9. Kumar, A. N. and Upadhye, N. S., On perturbations of Stein operator, Comm. Statist. Theory Methods, 46(18), 9284-9302, 2017. https://doi.org/10.1080/03610926.2016.1206937 

1. Kumar, A. N., Negative binomial approximation to sum of maxima of indicators, (under review).

1. Kumar A. N. and Upadhye, N. S., Pseudo-binomial approximation to (k1, k2)-runs, proceedings of 12th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2019), held at University of London, UK during December 14-16, 2019.

2. Kumar A. N. and Upadhye, N. S., Pseudo-binomial approximation to (1, 1)-runs, proceedings of International conference on computational physics, mathematics and its applications (ICCPMA 2016), held in Tokyo, Japan during November 7-8, 2016.

1. One day workshop on "Mathematics and its Engineering Applications" held at National Institute of Technology Calicut, October 26, 2018.

2. Workshop on "ATMW Applied Probability (2016)" held at Indian Institute of Technology Bombay during January 4-8, 2015.

1. Assistant Professor at the Department of Mathematical Sciences, IIT (BHU) Varanasi from November 22, 2022 to Till Date.

2. Visiting Assistant Professor at the Department of Mathematical Sciences, IIT (BHU) Varanasi from April 1, 2021 to November 21, 2022. 

3. Post Doctoral Fellow at the Department of Mathematics, IIT Bombay from December 10, 2018 to January 19,2021.

4. Ad-hoc Faculty at the Department of Mathematics, NIT Calicut from July 9, 2018 to December 05, 2018.

5. Post Doctoral Fellow at the Department of Mathematics, IIT Madras from December 01, 2017 to May 31, 2018.