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An Estimation Problem with Poisson Processes
Author(s) -
Gelfand Alan E.
Publication year - 1981
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1981.tb00780.x
Subject(s) - poisson distribution , categorical variable , poisson process , estimation , poisson regression , function (biology) , mathematics , statistics , intensity (physics) , compound poisson process , econometrics , computer science , physics , sociology , economics , demography , management , evolutionary biology , biology , quantum mechanics , population
Summary For n independent Poisson processes such that the i th process has intensity function lM i ( t ) =δ i ρ ( t ; α) we consider estimation of p ( t ; α) =∫ oρ: ( u ; α) du . Two procedures are developed, one using exact arrival times, the other using categorical arrival times. Two instances where p ( t ; α) = p(α t) are investigated further. An example applying the methodology to the active life of a judicial opinion is described.