Ruhul Ali Khan

Interests

Teaching

As an educator, my teaching philosophy revolves around creating a dynamic and engaging learning environment that caters to the diverse needs of students while leveraging modern teaching tools and technology. I firmly believe that effective teaching involves meticulous preparation, thoughtful resource provision, and a commitment to fostering a deep understanding of the subject matter.Utilizing modern teaching gadgets and technology is second nature to me. I incorporate these tools judiciously to enhance the clarity and impact of my presentations. By leveraging multimedia resources and interactive platforms, I aim to create an immersive learning experience that resonates with students.One of my core principles is to prepare well in advance of each class, ensuring that students have access to comprehensive resources throughout the course. I strive to go beyond traditional teaching methods by carefully selecting illustrative examples that vividly demonstrate the essential abstractions of the concepts. These examples serve as powerful tools to connect theoretical ideas with real-world applications, fostering a deeper understanding among students.Maintaining an interesting and well-paced classroom environment is paramount to me. I understand the importance of balancing the flow of knowledge, ensuring that students are both challenged and motivated. I actively encourage students to contemplate the applicability of the methods, fostering critical thinking and a deeper engagement with the subject matter.Teaching undergraduate courses, particularly those with interdisciplinary and diverse student backgrounds, presents a unique set of challenges. I believe it is the responsibility of the teacher to communicate materials effectively, especially to those who may struggle to assimilate complex concepts. To achieve this, I draw on my training in mathematics and statistics, leveraging my B.Sc. (Hons.) in Mathematics and M.Sc. in Applied Mathematics.I have successfully taught a range of courses, including MATH 464 Theory of Probability, DATA 366 Introduction to Multivariate Statistics, DATA 412 Linear Algebra for Data Science, and DATA 363 Introduction to Statistical Methods at Capital University of Economics and Business, Beijing. In these courses, I use my iPad to share content, taking a patient approach to accommodate non-native English speakers. I provide detailed typed lecture notes and weekly homework assignments, accompanied by comprehensive solutions, fostering a supportive learning environment.In the upcoming semesters, I will be instructing courses on Stochastic Process and Data Visualization. I am committed to continuous improvement and actively seek input from both colleagues and students. By utilizing feedback and drawing from my own experiences, I aim to enhance the learning experience for my students in every subsequent semester. Teaching, to me, is a dynamic and evolving process, and I am excited to continue contributing to the academic development of my students.

Research

My research interests are broadly in the area of Estimation Theory, Modelling (Statistical Methods & Theory), Nonparametric Statistics, Reliability Theory, Survival Analysis, Stochastic Ordering and ROC Curve Analysis.

Courses

Scholarly Contributions

Chapters

• Mitra, M., & Khan, R. A. (2021). Reliability Shock Models: A Brief Excursion. In Applied Advanced Analytics: 6th IIMA International Conference on Advanced Data Analysis, Business Analytics and Intelligence. doi:10.1007/978-981-33-6656-5_3
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  We attempt to provide a brief introduction to the extensive area of shock model research in reliability theory. Possible connections with application areas such as risk analysis, inventory control and biometry are indicated. Important concepts and tools for proving shock model results such as total positivity and variation diminishing property (VDP) are introduced. Most of the important results concerning nonparametric ageing classes arising from shock models are summarized, and some typical techniques of proof are emphasized. A variety of scenarios with diverse arrival processes such as homogeneous Poisson process, nonhomogeneous Poisson process, stationary and nonstationary pure birth processes are considered. A few interesting results related to cumulative damage models are also discussed.

Journals/Publications

• Bera, S., Bhattacharyya, D., Khan, R. A., & Mitra, M. (2023). Test for harmonic mean residual life function: A goodness of fit approach. Mathematics and Computers in Simulation. doi:10.1016/j.matcom.2022.06.008
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  A family of goodness of fit tests is proposed involving dominance in harmonic mean residual life (HMRL) order. We develop a test procedure based on a weighted integral approach. The test statistic proposed has been shown to be asymptotically normal — in addition the consistency of the proposed test has been established. Furthermore, the performance of the test has been assessed by means of a simulation study. Finally, we apply our test to a real-life dataset for purposes of illustration.
• Khan, R. A. (2023).

  Resilience Family of Receiver Operating Characteristic Curves

  . IEEE Transactions on Reliability. doi:10.1109/tr.2022.3194710
• Khan, R. A. (2023). Two-sample nonparametric test for proportional reversed hazards. Computational Statistics & Data Analysis. doi:10.1016/j.csda.2023.107708
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  In the last few decades, several works have been undertaken in the context of proportional reversed hazard rates (PRHR) but any specific statistical methodology for the PRHR hypothesis is absent in the literature. This paper proposes a two-sample nonparametric test based on two independent samples to verify the PRHR assumption. Based on a consistent U-statistic three statistical methodologies have been developed exploiting U-statistics theory, jackknife empirical likelihood and adjusted jackknife empirical likelihood method. A simulation study has been performed to assess the merit of the proposed test procedure. Finally, the proposed procedure is applied to a data set in the context of brain injury-related biomarkers and a data set related to Duchenne muscular dystrophy.
• Khan, R. A., Bhattacharyya, D., & Mitra, M. (2023). On some properties of distributions possessing a bathtub-shaped failure rate average. Journal of Applied Probability. doi:10.1017/jpr.2022.87
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2021). A goodness of fit test for mean time to failure function in age replacement. Journal of Statistical Computation and Simulation. doi:10.1080/00949655.2021.1944141
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2021). A new family of tests for DMTTF alternatives under complete and censored samples. Communications in Statistics-Simulation and Computation. doi:10.1080/03610918.2021.1965164
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  A family of nonparametric tests is proposed for detecting DMTTF property. The exact distributions of the test statistics are derived under the null hypothesis of exponentiality and critical values are calculated. The proposed test statistics are shown to be asymptotically normal and the consistency of the tests is established. Pitman asymptotic efficacy values are calculated. A large sample test under random censoring is also proposed and the relevant asymptotics are worked out. A Monte Carlo simulation study is carried out in order to assess the merit of the proposed tests. Finally, the test is applied to some real data sets for illustration.
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2021). Tests for Laplace order dominance with applications to insurance data. Insurance: Mathematics and Economics. doi:10.1016/j.insmatheco.2021.04.005
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  Tests for Laplace order dominance are proposed in the contexts of both one-sample and two-sample problems utilizing a weighted integral as measure of deviation. The concerned test statistics are shown to be asymptotically normal and consistency of both the tests is established. The performance of the proposed test procedures is assessed by means of a simulation study. Finally, the tests are applied to insurance data for illustrative purposes and actuarial implications derived from the tests are also presented.
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2021). Two-sample nonparametric test for comparing mean time to failure functions in age replacement. Journal of Statistical Planning and Inference. doi:10.1016/j.jspi.2020.10.003
• Khan, R. A., Bhattacharyya, D., & Mitra, M. (2021). Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives. Statistical Papers. doi:10.1007/s00362-021-01226-3
• Khan, R. A., Bhattacharyya, D., & Mitra, M. (2021). On classes of life distributions based on the mean time to failure function. Journal of Applied Probability. doi:10.1017/jpr.2020.91
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  Abstract The performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.
• Khan, R. A., Bhattacharyya, D., & Mitra, M. (2021). On some properties of the mean inactivity time function. Statistics & Probability Letters. doi:10.1016/j.spl.2020.108993
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2020). A nonparametric test for comparison of mean past lives. Statistics & Probability Letters. doi:10.1016/j.spl.2020.108722
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  Abstract A flexible nonparametric two sample test is developed for comparing Mean Past Lives (MPL) of two life distributions. The test is shown to be consistent having prescribed asymptotic size. We further develop an efficient algorithm for computing the test statistic. Finally, the performance of the test is assessed by means of a simulation study.
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2020). A test of exponentiality against DMTTF alternatives via L-statistics. Statistics & Probability Letters. doi:10.1016/j.spl.2020.108853
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  A consistent test for detecting DMTTF property is proposed. The exact null distribution of the test statistic as well as its asymptotic distribution have been derived. Efficacy values are calculated, and a simulation study is carried out to assess the performance of the test. Finally, the test is applied to some real-life data sets.
• Bhattacharyya, D., Khan, R. A., & Mitra, M. (2020). Stochastic comparisons of series, parallel and k-out-of-n systems with heterogeneous bathtub failure rate type components. Physica A: Statistical Mechanics and its Applications. doi:10.1016/j.physa.2019.123124
• Khan, R. A., Bhattacharyya, D., & Mitra, M. (2020). A change point estimation problem related to age replacement policies. Operations Research Letters. doi:10.1016/j.orl.2019.12.005
• Khan, R. A., & Mitra, M. (2019). Estimation issues in the Exponential–Logarithmic model under hybrid censoring. Statistical Papers. doi:10.1007/s00362-019-01100-3