LEADER 03968nam 22006015 450 001 9910743684103321 005 20250604142800.0 010 $a9783031370540 010 $a3031370546 024 7 $a10.1007/978-3-031-37054-0 035 $a(MiAaPQ)EBC30728641 035 $a(Au-PeEL)EBL30728641 035 $a(DE-He213)978-3-031-37054-0 035 $a(PPN)272737321 035 $a(CKB)28152184000041 035 $a(OCoLC)1396699209 035 $a(EXLCZ)9928152184000041 100 $a20230904d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntroduction to the Statistics of Poisson Processes and Applications /$fby Yury A. Kutoyants 205 $a1st ed. 2023. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2023. 215 $a1 online resource (683 pages) 225 1 $aFrontiers in Probability and the Statistical Sciences,$x2624-9995 311 08$aPrint version: Kutoyants, Yury A. Introduction to the Statistics of Poisson Processes and Applications Cham : Springer International Publishing AG,c2023 9783031370533 327 $aPoisson Processes -- Parameter Estimation -- Non-parametric Estimation -- Hypothesis Testing -- Applications -- Likelihood ratio and properties of MLE and BE. 330 $aThis book covers an extensive class of models involving inhomogeneous Poisson processes and deals with their identification, i.e. the solution of certain estimation or hypothesis testing problems based on the given dataset. These processes are mathematically easy-to-handle and appear in numerous disciplines, including astronomy, biology, ecology, geology, seismology, medicine, physics, statistical mechanics, economics, image processing, forestry, telecommunications, insurance and finance, reliability, queuing theory, wireless networks, and localisation of sources. Beginning with the definitions and properties of some fundamental notions (stochastic integral, likelihood ratio, limit theorems, etc.), the book goes on to analyse a wide class of estimators for regular and singular statistical models. Special attention is paid to problems of change-point type, and in particular cusp-type change-point models, then the focus turns to the asymptotically efficient nonparametric estimation of the mean function, the intensity function, and of some functionals. Traditional hypothesis testing, including some goodness-of-fit tests, is also discussed. The theory is then applied to three classes of problems: misspecification in regularity (MiR),corresponding to situations where the chosen change-point model and that of the real data have different regularity; optical communication with phase and frequency modulation of periodic intensity functions; and localization of a radioactive (Poisson) source on the plane using K detectors. Each chapter concludes with a series of problems, and state-of-the-art references are provided, making the book invaluable to researchers and students working in areas which actively use inhomogeneous Poisson processes. 410 0$aFrontiers in Probability and the Statistical Sciences,$x2624-9995 606 $aStatistics 606 $aNonparametric statistics 606 $aStatistical Theory and Methods 606 $aNon-parametric Inference 606 $aProcessos de Poisson$2thub 608 $aLlibres electrònics$2thub 615 0$aStatistics. 615 0$aNonparametric statistics. 615 14$aStatistical Theory and Methods. 615 24$aNon-parametric Inference. 615 7$aProcessos de Poisson 676 $a519.23 676 $a519.23 700 $aKutoyants$b Yury A$0442032 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910743684103321 996 $aIntroduction to the Statistics of Poisson Processes and Applications$93560138 997 $aUNINA