Foundations of Mathematical Analysis for Statistics

Mathematical analysis forms the rigorous backbone of modern statistics, enabling a precise understanding of continuity, differentiability, integration, and convergence, all of which are central to probability theory, inference, stochastic processes, and machine learning. As the boundaries between pure mathematics and statistical applications continue to dissolve, a solid foundation in analysis becomes not just desirable but indispensable for serious students of statistics. This book, Foundations of Mathematical Analysis for Statistics, is the result of years of teaching and research, distilled into a coherent and structured resource intended for graduate and advanced undergraduate students in statistics, mathematics, and allied disciplines. It bridges classical real and complex analysis with the analytical tools used in contemporary statistical theory and modeling.

Autorentext

Dr. Janardan Behera is an Assistant Professor in the Department of Statistics at Ravenshaw University, where he has been teaching and guiding students in theoretical and applied statistics. With a strong background in mathematical analysis, his academic interests include real and complex analysis, probability theory, and statistical inference.