Introduction to the Statistics of Poisson Processes and Applications - Yury A. Kutoyants

Introduction to the Statistics of Poisson Processes and Applications

Buch | Hardcover
XXIII, 666 Seiten
2023 | 2023
Springer International Publishing (Verlag)
978-3-031-37053-3 (ISBN)
160,49 inkl. MwSt

This book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources.

Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors.

Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes.

Poisson Processes.- Parameter Estimation.- Non-parametric Estimation.- Hypothesis Testing.- Applications.- Likelihood ratio and properties of MLE and BE.

Erscheinungsdatum
Reihe/Serie Frontiers in Probability and the Statistical Sciences
Zusatzinfo XXIII, 666 p. 51 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 1196 g
Themenwelt Mathematik / Informatik Mathematik Statistik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte change-point problems • Misspecifications • nonparametric estimation • Parameter Estimation • Poisson Processes • Source Localization
ISBN-10 3-031-37053-8 / 3031370538
ISBN-13 978-3-031-37053-3 / 9783031370533
Zustand Neuware
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