Journal of Applied Probability: Volume 44 - Issue 4

Fixation in Conditional Branching Process Models in Population Genetics
Part of:
- Markov processes
Thomas Prince, Neville Weber
Published online by Cambridge University Press:

14 July 2016, pp. 1103-1110
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An alternative version of the necessary and sufficient condition for almost sure fixation in the conditional branching process model is derived. This formulation provides an insight into why the examples considered in Buckley and Seneta (1983) all have the same condition for fixation.

Tail Asymptotics for the Queue Size Distribution in an M/G/1 Retrial Queue
Part of:
- Special processes
Jerim Kim, Bara Kim, Sung-Seok Ko
Published online by Cambridge University Press:

14 July 2016, pp. 1111-1118
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We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

Negative Association Does not Imply Log-Concavity of the Rank Sequence
Part of:
- Distribution theory - Probability
- Multivariate analysis
Klas Markström
Published online by Cambridge University Press:

14 July 2016, pp. 1119-1121
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We present a minimum counterexample to the conjecture that a negatively associated random variable has an ultra-log-concave rank sequence. The rank sequence does not in fact even need to be unimodal.

Journal of Applied Probability