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- W2317360039 abstract "Let Y 0 , Y 1 , Y 2 , … be an i.i.d. sequence of random variables with continuous distribution function, and let P be a simple point process on 0≦ t ≦∞, independent of the Y j ' s. We assume that P has a point at t = 0; we associate Y j with the j th point of j ≧0, and we say that the Y j 's occur at the arrival times of P . Y 0 is considered a ‘reference value'. The first Y j ( j ≧1) to exceed all previous ones is called the first ‘record value', and the time of its occurrence is the first ‘record time'. Subsequent record values and times are defined analogously. We give an infinite series representation for the joint characteristic function of the first n record times, for general P ; in some cases the series can be summed. We find the intensity of the record process when P is a general birth process, and when P is a linear birth process with m immigration sources we find the distribution of the number of records in (0, t ]. For m = 0 (the Yule process) we give moments of record times and a compact form for the record process intensity. We show that the records occur according to a homogeneous Poisson process when m = 1, and we display a different model with the same behavior, leading to statistical non-identifiability if only the record times are observed. For m = 2, the records occur according to a semi-Markov process; again we display a different model with the same behavior. Finally we give a new derivation of the joint distribution of the interrecord times when P is an arbitrary Poisson process. We relate this result to existing work and to the classical record model. We also obtain a new characterization of the exponential distribution." @default.
- W2317360039 created "2016-06-24" @default.
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- W2317360039 date "1992-03-01" @default.
- W2317360039 modified "2023-10-18" @default.
- W2317360039 title "Exact distribution theory for some point process record models" @default.
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- W2317360039 doi "https://doi.org/10.2307/1427728" @default.
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