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THE SOJOURN TIME DISTRIBUTION OF AN ALTERNATING RENEWAL PROCESS
Author(s) -
Rossiter M.H.
Publication year - 1989
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.1989.tb00508.x
Subject(s) - laplace transform , renewal theory , first hitting time model , state (computer science) , distribution (mathematics) , mathematics , process (computing) , statistical physics , stochastic process , calculus (dental) , computer science , mathematical analysis , algorithm , statistics , physics , medicine , dentistry , operating system
summary Ordinary, modified, and equilibrium alternating renewal processes are defined in such a way that the distribution of the sojourn time in one state of a two‐state system may be considered conditional on the starting state. The double Laplace transform of a non‐negative stochastic process is also defined, and used to express a result of Takacs (1957) on sojourn time distributions.