DFR (Decreasing Failure Rate) Property of First Passage Times and Its Preservation under Geometric Compounding.

1986 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Failure Rate ◽  
First Passage Times ◽  
First Passage ◽  
Decreasing Failure Rate ◽  
Rate Property ◽  
Passage Times

Total Positivity of Markov Chains and the Failure Rate Character of Some First Passage Times

1997 ◽  
Vol 29 (3) ◽  
pp. 713-732 ◽  
Author(s):  
Shiowjen Lee ◽  
J. Lynch
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Failure Rate ◽  
Total Positivity ◽  
First Passage Times ◽  
First Passage ◽  
Positive Order ◽  
Totally Positive ◽  
Ordered State ◽  
Passage Times

It is shown that totally positive order 2 (TP2) properties of the infinitesimal generator of a continuous-time Markov chain with totally ordered state space carry over to the chain's transition distribution function. For chains with such properties, failure rate characteristics of the first passage times are established. For Markov chains with partially ordered state space, it is shown that the first passage times have an IFR distribution under a multivariate total positivity condition on the transition function.

On the first-passage times of pure jump processes

1988 ◽  
Vol 25 (3) ◽  
pp. 501-509 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Jump Process ◽  
First Passage Times ◽  
Jump Processes ◽  
First Passage ◽  
Increasing Failure Rate ◽  
Passage Times

Let Tx be the time it takes for a pure jump process, which starts at 0, to cross a threshold x > 0. Sufficient conditions on the parameters of this process under which Tx has increasing failure rate average (IFRA), increasing failure rate (IFR) or logconcave density (PF2) are identified. The conditions for IFRA are weaker than those of Drosen (1986). Sufficient conditions on the parameter of a pure jump process for Tx to the IFR or PF2 are not available in the literature.

On the first-passage times of pure jump processes

1988 ◽  
Vol 25 (03) ◽  
pp. 501-509 ◽  
Author(s):  
Moshe Shared ◽  
J. George Shanthikumar
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Jump Process ◽  
First Passage Times ◽  
Jump Processes ◽  
First Passage ◽  
Increasing Failure Rate ◽  
Passage Times

Let Tx be the time it takes for a pure jump process, which starts at 0, to cross a threshold x > 0. Sufficient conditions on the parameters of this process under which Tx has increasing failure rate average (IFRA), increasing failure rate (IFR) or logconcave density (PF2) are identified. The conditions for IFRA are weaker than those of Drosen (1986). Sufficient conditions on the parameter of a pure jump process for Tx to the IFR or PF2 are not available in the literature.

Total Positivity of Markov Chains and the Failure Rate Character of Some First Passage Times

1997 ◽  
Vol 29 (03) ◽  
pp. 713-732 ◽  
Author(s):  
Shiowjen Lee ◽  
J. Lynch
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Failure Rate ◽  
Total Positivity ◽  
First Passage Times ◽  
First Passage ◽  
Positive Order ◽  
Totally Positive ◽  
Ordered State ◽  
Passage Times

It is shown that totally positive order 2 (TP2) properties of the infinitesimal generator of a continuous-time Markov chain with totally ordered state space carry over to the chain's transition distribution function. For chains with such properties, failure rate characteristics of the first passage times are established. For Markov chains with partially ordered state space, it is shown that the first passage times have an IFR distribution under a multivariate total positivity condition on the transition function.

Inequalities for Means of Restricted First-Passage Times in Percolation Theory

1999 ◽  
Vol 8 (4) ◽  
pp. 307-315 ◽  
Author(s):  
SVEN ERICK ALM ◽  
JOHN C. WIERMAN
Keyword(s):  
Half Space ◽  
Percolation Theory ◽  
First Passage Times ◽  
First Passage ◽  
Geometric Argument ◽  
Convexity And Concavity ◽  
Passage Times

A simple geometric argument establishes an inequality between the sums of two pairs of first-passage times. This result is used to prove monotonicity, convexity and concavity results for first-passage times with cylinder and half-space restrictions.

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