Journal Article10.1239/JAP/1014842834
On some waiting time problems
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TL;DR: In this article, a unifying technology for finding explicit closed form expressions for joint moment generating functions of various random quantities associated with some waiting time problems is introduced, and later waiting times are covered for general discrete-and continuous-time models.
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Abstract: A unifying technology is introduced for finding explicit closed form expressions for joint moment generating functions of various random quantities associated with some waiting time problems. Sooner and later waiting times are covered for general discrete- and continuous-time models. The models are either Markov chains or semi-Markov processes with a finite number of states. Waiting times associated with generalized phase-type distributions, that are of interest in survival analysis and other areas, are also covered.
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References
•Journal Article
Phase type distributions in survival analysis
TL;DR: In this article, a finite-state, time-continuous, homogeneous Markov chain with an absorbing state is considered and the time to absorption in such a state is said to have a phase-type distribution.
125
Sooner and later waiting time problems for Bernoulli trials: frequency and run quotas
M. Ebneshahrashoob,Milton Sobel +1 more
TL;DR: For a sequence of independent Bernoulli trials with probabilities of success and failure p and q respectively, the sooner and later waiting time random variables for the succession quota (s successes and r failures) are studied by deriving a generalized pgf and obtaining the means and variances as discussed by the authors.
102
Sooner and later waiting time problems for Markovian Bernoulli trials
TL;DR: In this paper, the waiting time problems introduced by Ebneshahrashoob and Sobel (1990) for independent trials are generalized to Markov correlated Bernoulli trials.
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