Closure and montonocity properties of nonhomogeneous poisson processes and record values

1988 ◽

Vol 2 (4) ◽

pp. 475-484 ◽

Cited By ~ 67

Author(s):

Ramesh C. Gupta ◽

S.N.U.A. Kirmani

Keyword(s):

Value Function ◽

Record Values ◽

Mean Value ◽

Poisson Processes ◽

Minimal Repair ◽

Nonhomogeneous Poisson Processes ◽

Upper Record Values ◽

The Mean ◽

Upper Record ◽

Occurrence Times

Interconnections between occurrence times of nonhomogeneous Poisson processes, record values, minimal repair times, and the relevation transform are explained. A number of properties of the distributions of occurrence times and interoccurrence times of a nonhomogeneous Poisson process are proved when the mean-value function of the process is convex, starshaped, or superadditive. The same results hold for upper record values of independently identically distributed random variables from IFR, IFRA, and NBU distributions.

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A Note on Dispersive Ordering of Record Values

Calcutta Statistical Association Bulletin ◽

10.1177/0008068319960106 ◽

1996 ◽

Vol 46 (1-2) ◽

pp. 63-68 ◽

Cited By ~ 6

Author(s):

Subhash C. Kochar

Keyword(s):

Record Values ◽

Intensity Function ◽

Poisson Processes ◽

Nonhomogeneous Poisson Processes ◽

Dispersive Ordering ◽

Occurrence Times

It is proved that the successive record values from a DFR distribution are more dispersed. Because of the connection between record values and the occurrence times of a nonhomogeneous Poisson processes (NHPP) it proves that when the intensity function of an NHPP is nonincreasina, the successive occurrence times are more dispersed.

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NONHOMOGENEOUS POISSON PROCESSES AND LOGCONCAVITY

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964800143062 ◽

2000 ◽

Vol 14 (3) ◽

pp. 353-373 ◽

Cited By ~ 40

Author(s):

Franco Pellerey ◽

Moshe Shaked ◽

Joel Zinn

Keyword(s):

Poisson Process ◽

Discrete Time ◽

Record Values ◽

Nonhomogeneous Poisson Process ◽

Poisson Processes ◽

Counting Processes ◽

Minimal Repair ◽

Discrete Probability ◽

Nonhomogeneous Poisson Processes ◽

Probability Densities

In this article, we identify conditions under which the epoch times and the interepoch intervals of a nonhomogeneous Poisson process have logconcave densities. The results are extended to relevation counting processes. We also study discrete-time counting processes and find conditions under which the epoch times and the interepoch intervals of these discrete-time processes have logconcave discrete probability densities. The results are interpreted in terms of minimal repair and record values. Several examples illustrate the theory.

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