The IFR/DFR property of the forward recurrence-time distribution

1998 ◽  
Vol 47 (1) ◽  
pp. 59-65 ◽  
Author(s):  
H. Polatioglu ◽  
I. Sahin
Keyword(s):  
Time Distribution ◽  
Recurrence Time ◽  
Forward Recurrence Time

The theory of periodic screening I: Lead time and proportion detected

1976 ◽  
Vol 8 (1) ◽  
pp. 127-143 ◽  
Author(s):  
Philip C. Prorok
Keyword(s):  
Chronic Disease ◽  
Natural History ◽  
Time Distribution ◽  
Lead Time ◽  
Screening Program ◽  
Clinical State ◽  
Recurrence Time ◽  
Sojourn Time Distribution ◽  
History Of ◽  
Forward Recurrence Time

A stochastic model for a periodic screening program is presented in which the natural history of a chronic disease is assumed to follow a progressive path from a preclinical state to a clinical state. The sampling of preclinical state sojourn times by screening examinations generates bounds on the preclinical state recurrence times. The distribution of the bounded forward recurrence time is derived and used to obtain the distribution and mean of the lead time, and relationships for calculating the proportion of preclinical cases detected. These expressions are derived in terms of the preclinical state sojourn-time distribution and adjustible parameters important in the design of a periodic screening program.

Some non-stationary point processes with stationary forward recurrence time distribution

1975 ◽  
Vol 12 (1) ◽  
pp. 167-169 ◽  
Author(s):  
Mats Rudemo
Keyword(s):  
Stationary Point ◽  
Time Distribution ◽  
Point Processes ◽  
Recurrence Time ◽  
Renewal Processes ◽  
Forward Recurrence Time ◽  
Stationary Point Processes

Examples are given of point processes that are non-stationary but have stationary forward recurrence time distributions. They are obtained by modification of stationary Poisson and renewal processes.

The theory of periodic screening I: Lead time and proportion detected

1976 ◽  
Vol 8 (01) ◽  
pp. 127-143 ◽  
Author(s):  
Philip C. Prorok
Keyword(s):  
Chronic Disease ◽  
Natural History ◽  
Time Distribution ◽  
Lead Time ◽  
Screening Program ◽  
Clinical State ◽  
Recurrence Time ◽  
Sojourn Time Distribution ◽  
History Of ◽  
Forward Recurrence Time

A stochastic model for a periodic screening program is presented in which the natural history of a chronic disease is assumed to follow a progressive path from a preclinical state to a clinical state. The sampling of preclinical state sojourn times by screening examinations generates bounds on the preclinical state recurrence times. The distribution of the bounded forward recurrence time is derived and used to obtain the distribution and mean of the lead time, and relationships for calculating the proportion of preclinical cases detected. These expressions are derived in terms of the preclinical state sojourn-time distribution and adjustible parameters important in the design of a periodic screening program.

Some non-stationary point processes with stationary forward recurrence time distribution

1975 ◽  
Vol 12 (01) ◽  
pp. 167-169
Author(s):  
Mats Rudemo
Keyword(s):  
Stationary Point ◽  
Time Distribution ◽  
Point Processes ◽  
Recurrence Time ◽  
Renewal Processes ◽  
Forward Recurrence Time ◽  
Stationary Point Processes

Examples are given of point processes that are non-stationary but have stationary forward recurrence time distributions. They are obtained by modification of stationary Poisson and renewal processes.

scholarly journals Nonparametric Estimation of the Bivariate Recurrence Time Distribution

Biometrics ◽  
2005 ◽  
Vol 61 (2) ◽  
pp. 392-402 ◽  
Author(s):  
Chiung-Yu Huang ◽  
Mei-Cheng Wang
Keyword(s):  
Nonparametric Estimation ◽  
Time Distribution ◽  
Recurrence Time

A note on stochastic decomposition in a GI/G/1 queue with vacations or set-up times

1985 ◽  
Vol 22 (02) ◽  
pp. 419-428 ◽  
Author(s):  
Bharat T. Doshi
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Sample Path ◽  
The Other ◽  
Independent Random Variables ◽  
Recurrence Time ◽  
Stochastic Decomposition ◽  
Set Up ◽  
Forward Recurrence Time ◽  
Main Model

In this note we prove some stochastic decomposition results for variations of theGI/G/1 queue. Our main model is aGI/G/1 queue in which the server, when it becomes idle, goes on a vacation for a random length of time. On return from vacation, if it finds customers waiting, then it starts serving the first customer in the queue. Otherwise it takes another vacation and so on. Under fairly general conditions the waiting time of an arbitrary customer, in steady state, is distributed as the sum of two independent random variables: one corresponding to the waiting time without vacations and the other to the stationary forward recurrence time of the vacation. This extends the decomposition result of Gelenbe and Iasnogorodski [5]. We use sample path arguments, which are also used to prove stochastic decomposition in aGI/G/1 queue with set-up time.

Uniform limit theorems for non-singular renewal and Markov renewal processes

1978 ◽  
Vol 15 (1) ◽  
pp. 112-125 ◽  
Author(s):  
Elja Arjas ◽  
Esa Nummelin ◽  
Richard L. Tweedie
Keyword(s):  
Recurrence Time ◽  
Renewal Processes ◽  
Convergence Properties ◽  
Renewal Theorem ◽  
Uniform Limit ◽  
Markov Renewal Processes ◽  
Key Renewal Theorem ◽  
Positive Recurrent ◽  
Forward Recurrence Time ◽  
Initial Distributions

We show that if the increment distribution of a renewal process has some convolution non-singular with respect to Lebesgue measure, then the skeletons of the forward recurrence time process are φ-irreducible positive recurrent Markov chains. Known convergence properties of such chains give simple proofs of uniform versions of some old and new key renewal theorems; these show in particular that non-singularity assumptions on the increment and initial distributions enable the assumption of direct Riemann integrability to be dropped from the standard key renewal theorem. An application to Markov renewal processes is given.

Sign in / Sign up

Export Citation Format

Share Document