國立虎尾科技大學 |

Introduction to the statistics of Poisson processes and applications

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Introduction to the statistics of Poisson processes and applications/ by Yury A. Kutoyants.
Author:	Kutoyants, Yu A.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	xxiii, 666 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Non-parametric Inference. -
Online resource:	https://doi.org/10.1007/978-3-031-37054-0
ISBN:	9783031370540

Introduction to the statistics of Poisson processes and applications
Kutoyants, Yu A.

Introduction to the statistics of Poisson processes and applications[electronic resource] /by Yury A. Kutoyants. - Cham :Springer International Publishing :2023. - xxiii, 666 p. :ill., digital ;24 cm. - Frontiers in probability and the statistical sciences,2624-9995. - Frontiers in probability and the statistical sciences..

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

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.

ISBN: 9783031370540

Standard No.: 10.1007/978-3-031-37054-0doiSubjects--Topical Terms:

1366137
Non-parametric Inference.

LC Class. No.: QA274.42 / .K87 2023

Dewey Class. No.: 519.23

Introduction to the statistics of Poisson processes and applications
LDR:03002nam a2200337 a 4500 001 1116313
003 DE-He213
005 20230904223536.0
006 m d
007 cr nn 008maaau
008 240123s2023 sz s 0 eng d
020 $a 9783031370540 $q (electronic bk.)
020 $a 9783031370533 $q (paper)
024 7 $a 10.1007/978-3-031-37054-0 $2 doi
035 $a 978-3-031-37054-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.42 $b .K87 2023
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
082 0 4 $a 519.23 $2 23
090 $a QA274.42 $b .K97 2023
100 1 $a Kutoyants, Yu A. $3 1429510
245 1 0 $a Introduction to the statistics of Poisson processes and applications $h [electronic resource] / $c by Yury A. Kutoyants.
260 $a Cham : $c 2023. $b Springer International Publishing : $b Imprint: Springer,
300 $a xxiii, 666 p. : $b ill., digital ; $c 24 cm.
490 1 $a Frontiers in probability and the statistical sciences, $x 2624-9995
505 0 $a Poisson Processes -- Parameter Estimation -- Non-parametric Estimation -- Hypothesis Testing -- Applications -- Likelihood ratio and properties of MLE and BE.
520 $a 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.
650 2 4 $a Non-parametric Inference. $3 1366137
650 1 4 $a Statistical Theory and Methods. $3 671396
650 0 $a Poisson processes. $3 898219
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a Frontiers in probability and the statistical sciences. $3 1067403
856 4 0 $u https://doi.org/10.1007/978-3-031-37054-0
950 $a Mathematics and Statistics (SpringerNature-11649)