Ergodicity of statistical estimates of Poisson flow intensity |
Tsitsiashvili G.Sh. |
2019, issue 2, P. 256–260 |
Abstract |
This paper raises the question of how to transform the observation procedure to replace a long series of observations by several short and, conversely, several short series by one long. This problem is solved to assess the intensity of the stationary Poisson flow and to estimate the average time of operation of technical systems for failure using the concept of ergodicity of the observation process. |
Keywords: ergodicity, Poisson flow, exponential distribution, mean failure time |
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References |
[1] Iu.N. Kul'chin, “Fotonika samoorganizuiushchikhsia biomineral'nykh nanostruktur”, UFN, 181:8, (2011), 891–896. [2] V.B. Monsik, A.A. Skrynnikov, “Otsenivanie parametra pokazatel'nogo raspredeleniia po usechennoi vyborke”, Nauchnyi vestnik MGTU GA. Seriia prikladnaia matematika. Informatika, 105, (2006), 134–139. [3] F.N. Il'iasov, “Obratnaia zadacha vyborki i motivatsiia na rynke Foreks”, Sotsiologicheskie issledovaniia, 3, (2011), 112–116. [4] F.N. Il'iasov, “Reprezentativnost' rezul'tatov oprosa v marketingovom issledovanii”, Sotsial'nye issledovaniia, 2, (2016), 49–59. [5] B.I. Semkin, “Ob invariantnosti srednikh otnoshenii velichin (na primere nekotorykh morfologicheskikh priznakov sloevishch laminarii iaponskoi (Laminaria japonica Aresh.) iz sublitorali Severnogo Primor'ia”, Izvestiia TINRO, 171, (2012), 313–320. [6] J. von Neumann, “Physical Applications of the Ergodic Hypothesis”, Proc Natl Acad Sci USA, 18, (1932), 263–266. [7] A.Ia. Khinchin, Matematicheskie osnovy statisticheskoi mekhaniki, OGIZ. Gos. izd-vo tekhniko-teoret. lit., Moskva, 1943. [8] I.P. Kornfel'd, Ia.G. Sinai, S.V. Fomin, Ergodicheskaia teoriia, Nauka, Moskva, 1980. [9] A.Ia. Khinchin, Raboty po teorii matematicheskoi teorii massovogo obsluzhivaniia, Fizmatlit, Moskva, 1963. [10] A.A. Borovkov, Kurs teorii veroiatnostei, Nauka, Moskva, 1972. [11] A.Ia. Khinchin, Tsepnye drobi, Fizmatlit, Moskva–Leningrad, 1949. |