Closure and Monotonicity Properties of Nonhomogeneous Poisson Processes and Record Values

1988 ◽  
Vol 2 (4) ◽  
pp. 475-484 ◽  
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.

Extremal processes and random measures

1975 ◽  
Vol 12 (2) ◽  
pp. 316-323 ◽  
Author(s):  
R. W. Shorrock
Keyword(s):  
Random Measure ◽  
Record Values ◽  
Poisson Processes ◽  
Two Dimensional ◽  
Random Measures ◽  
Record Times ◽  
Upper Record Values ◽  
Extremal Processes ◽  
Upper Record ◽  
Gamma Processes

Discrete time extremal processes with a continuous underlying c.d.f. are random measures which can be viewed as two-dimensional Poisson processes and this representation is used to obtain the conditional law of the sequence of states the process passes through (upper record values) given the sequence of holding times in states (inter-record times). In addition the Gamma processes (which lead to the Ferguson Dirichlet processes) and a random measure that arises in sampling from a biological population are discussed as two-dimensional Poisson processes.

A Note on Dispersive Ordering of Record Values

1996 ◽  
Vol 46 (1-2) ◽  
pp. 63-68 ◽  
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.

NONHOMOGENEOUS POISSON PROCESSES AND LOGCONCAVITY

2000 ◽  
Vol 14 (3) ◽  
pp. 353-373 ◽  
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.

Extremal processes and random measures

1975 ◽  
Vol 12 (02) ◽  
pp. 316-323
Author(s):  
R. W. Shorrock
Keyword(s):  
Random Measure ◽  
Record Values ◽  
Poisson Processes ◽  
Two Dimensional ◽  
Random Measures ◽  
Record Times ◽  
Upper Record Values ◽  
Extremal Processes ◽  
Upper Record ◽  
Gamma Processes

Discrete time extremal processes with a continuous underlying c.d.f. are random measures which can be viewed as two-dimensional Poisson processes and this representation is used to obtain the conditional law of the sequence of states the process passes through (upper record values) given the sequence of holding times in states (inter-record times). In addition the Gamma processes (which lead to the Ferguson Dirichlet processes) and a random measure that arises in sampling from a biological population are discussed as two-dimensional Poisson processes.

scholarly journals Some Characterizations of the Distribution of the Condition Number of a Complex Gaussian Matrix

2020 ◽  
Vol 8 (1) ◽  
pp. 22-35
Author(s):  
M. Shakil ◽  
M. Ahsanullah
Keyword(s):  
Order Statistics ◽  
Condition Number ◽  
Record Values ◽  
Distributional Properties ◽  
Upper Record Values ◽  
Upper Record

AbstractThe objective of this paper is to characterize the distribution of the condition number of a complex Gaussian matrix. Several new distributional properties of the distribution of the condition number of a complex Gaussian matrix are given. Based on such distributional properties, some characterizations of the distribution are given by truncated moment, order statistics and upper record values.

scholarly journals Nonparametric Prediction Intervals of generalized order statistics from two independent sequences

2016 ◽  
Vol 4 (1) ◽  
pp. 36 ◽  
Author(s):  
Mostafa Mohie El-Din ◽  
Walid Emam
Keyword(s):  
Order Statistics ◽  
Record Values ◽  
Prediction Intervals ◽  
Generalized Order Statistics ◽  
Special Cases ◽  
Upper Record Values ◽  
Upper Record ◽  
Nonparametric Prediction ◽  
Nonparametric Prediction Intervals ◽  
Generalized Order

<p>This paper, discusses the problem of predicting future a generalized order statistic of an iid sequence sample was drawn from an arbitrary unknown distribution, based on observed also generalized order statistics from the same population. The coverage probabilities of these prediction intervals are exact and free of the parent distribution F(). Prediction formulas of ordinary order statistics and upper record values are extracted as special cases from the productive results. Finally, numerical computations on several models of ordered random variables are given to illustrate the proposed procedures.</p>

Realisation of the mean-value function

1973 ◽  
Vol 9 (22) ◽  
pp. 528
Author(s):  
E. Ball
Keyword(s):  
Value Function ◽  
Mean Value ◽  
The Mean

scholarly journals Evaluating the Lifetime Performance Index Based on the Bayesian Estimation for the Rayleigh Lifetime Products with the Upper Record Values

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Wen-Chuan Lee ◽  
Jong-Wuu Wu ◽  
Ching-Wen Hong ◽  
Shie-Fan Hong
Keyword(s):  
Loss Function ◽  
Performance Index ◽  
Resource Planning ◽  
Record Values ◽  
Testing Procedure ◽  
Assessment System ◽  
Squared Error Loss Function ◽  
Lifetime Performance ◽  
Upper Record Values ◽  
Upper Record

Quality management is very important for many manufacturing industries. Process capability analysis has been widely applied in the field of quality control to monitor the performance of industrial processes. Hence, the lifetime performance indexCLis utilized to measure the performance of product, whereLis the lower specification limit. This study constructs a Bayesian estimator ofCLunder a Rayleigh distribution with the upper record values. The Bayesian estimations are based on squared-error loss function, linear exponential loss function, and general entropy loss function, respectively. Further, the Bayesian estimators ofCLare utilized to construct the testing procedure forCLbased on a credible interval in the condition of knownL. The proposed testing procedure not only can handle nonnormal lifetime data, but also can handle the upper record values. Moreover, the managers can employ the testing procedure to determine whether the lifetime performance of the Rayleigh products adheres to the required level. The hypothesis testing procedure is a quality performance assessment system in enterprise resource planning (ERP).

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