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- W2313532661 abstract "It is shown that if a finite-state continuous-time Markov process can be uniformized such that the embedded Markov chain has a TP r (totally positive of order r ) transition matrix, then the first-passage time from state 0 to any other state has a PF r (Polya frequency of order r ) density. As a consequence, results of Keilson (1971), Esary, Marshall and Proschan (1973), Ghosh and Ebrahimi (1982) and Derman, Ross and Schechner (1983) are strengthened. It is also shown that some cumulative damage shock models, with an underlying compound Poisson process and ‘damages' which are not necessarily non-negative, are associated with wear processes having PF r first-passage times to any threshold. First-passage times with completely monotone densities are also discussed." @default.
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- W2313532661 date "1985-03-01" @default.
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- W2313532661 title "First-passage times with PF<sub><i>r</i></sub> densities" @default.
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- W2313532661 doi "https://doi.org/10.2307/3213758" @default.
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