Extreme-value properties of the explosion-time distribution in a pure birth process
- 1 September 1982
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 19 (3) , 500-509
- https://doi.org/10.2307/3213509
Abstract
In each of a large number N of independent cells a breakdown mechanism is under way and proceeds until the first of the cells actually fails. At such a time, in each cell, the situation reverts to some initial state and the mechanism restarts. In this paper we consider those mechanisms for which breakdown may be modelled as the explosion of a pure birth process. Of interest is the distribution of time between failures and the possibility of estimating N and/or model parameters by observing a sequence of failure times. Saddlepoint approximation methods are used in the relevant extreme-value theory analysis for two important cases.Keywords
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