Bayesian estimation of renewal function for inverse Gaussian renewal process

2011 ◽  
Vol 81 (3) ◽  
pp. 331-341 ◽  
Author(s):  
M. S. Aminzadeh
Keyword(s):  
Bayesian Estimation ◽  
Renewal Process ◽  
Inverse Gaussian ◽  
Renewal Function

Some results involving HNBUE distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1038-1044
Author(s):  
A. P. Basu ◽  
S. N. U. A. Kirmani
Keyword(s):  
Lower Bound ◽  
Exponential Distribution ◽  
Renewal Process ◽  
Renewal Function ◽  
Underlying Distribution

A characterization of the exponential distribution in the class of all distributions which are HNBUE or HNWUE is proved. An upper (a lower) bound is obtained on the renewal function of a renewal process when the underlying distribution is HNBUE (HNWUE).

Monte Carlo simulation of the renewal function

1981 ◽  
Vol 18 (2) ◽  
pp. 426-434 ◽  
Author(s):  
Mark Brown ◽  
Herbert Solomon ◽  
Michael A. Stephens
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Renewal Process ◽  
Time Distribution ◽  
Interarrival Time ◽  
Renewal Function ◽  
Expected Number ◽  
Unbiased Estimators ◽  
Monte Carlo Estimation ◽  
Naive Estimator

The problem of Monte Carlo estimation of M(t) = EN(t), the expected number of renewals in [0, t] for a renewal process with known interarrival time distribution F, is considered. Several unbiased estimators which compete favorably with the naive estimator, N(t), are presented and studied. An approach to reduce the variance of the Monte Carlo estimator is developed and illustrated.

Characterizing pure loss GI/G/1 queues with renewal output

1974 ◽  
Vol 75 (1) ◽  
pp. 103-107 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Poisson Process ◽  
Service Time ◽  
Renewal Process ◽  
Queueing System ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Arrival Process ◽  
Renewal Function ◽  
Service Distribution ◽  
Necessary And Sufficient

SummaryIn a pure loss GI/G/1 queueing system, necessary and sufficient conditions are given for the output to be a renewal process. These conditions involve dependence between the service distribution and the renewal function of the arrival process: for example, if pr {service time < ξ} = 0 for some ξ > 0, then it is sufficient for the renewal function to be that of a quasi-Poisson process with index ξ.

Some results involving HNBUE distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1038-1044 ◽  
Author(s):  
A. P. Basu ◽  
S. N. U. A. Kirmani
Keyword(s):  
Lower Bound ◽  
Exponential Distribution ◽  
Renewal Process ◽  
Renewal Function ◽  
Underlying Distribution

A characterization of the exponential distribution in the class of all distributions which are HNBUE or HNWUE is proved. An upper (a lower) bound is obtained on the renewal function of a renewal process when the underlying distribution is HNBUE (HNWUE).

Some results involving HNBUE distributions

1986 ◽  
Vol 23 (4) ◽  
pp. 1038-1044 ◽  
Author(s):  
A. P. Basu ◽  
S. N. U. A. Kirmani
Keyword(s):  
Lower Bound ◽  
Exponential Distribution ◽  
Renewal Process ◽  
Renewal Function ◽  
Underlying Distribution

A characterization of the exponential distribution in the class of all distributions which are HNBUE or HNWUE is proved. An upper (a lower) bound is obtained on the renewal function of a renewal process when the underlying distribution is HNBUE (HNWUE).

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