Waiting time distributions of success runs of length r and failure runs of length r'

2002 ◽  
Vol 39 (1-2) ◽  
pp. 75-85
Author(s):  
K. Sen ◽  
M. Agarwal ◽  
B. Goyal
Keyword(s):  
Waiting Time ◽  
Success Runs ◽  
Waiting Time Distributions

Lengths of runs and waiting time distributions by using Pólya-Eggenberger sampling scheme

2002 ◽  
Vol 39 (3-4) ◽  
pp. 309-332 ◽  
Author(s):  
K. Sen ◽  
Manju L. Agarwal ◽  
S. Chakraborty
Keyword(s):  
Waiting Time ◽  
Lattice Path ◽  
Sampling Scheme ◽  
Bernoulli Trials ◽  
Success Runs ◽  
Waiting Time Distributions ◽  
Joint Distributions ◽  
First Occurrence

In this paper, joint distributions of number of success runs of length k and number of failure runs of length k' are obtained by using combinatorial techniques including lattice path approach under Pólya-Eggenberger model. Some of its particular cases, for different values of the parameters, are derived. Sooner and later waiting time problems and joint distributions of number of success runs of various types until first occurrence of consecutive success runs of specified length under the model are obtained. The sooner and later waiting time problems for Bernoulli trials (see Ebneshahrashoob and Sobel [3]) and joint distributions of the type discussed by Uchiada and Aki [11] are shown as particular cases. Assuming Ln and Sn to be the lengths of longest and smallest success runs, respectively, in a sample of size n drawn by Pólya-Eggenberger sampling scheme, the joint distributions of Ln and  Sn as well as distribution of M=max(Ln,Fn)n, where Fn is the length of longest failure run, are also  obtained.

AGE DATING SEDIMENT TO ESTABLISH GEOCHRONOLOGY OF MID-ATLANTIC FLOODPLAINS AND SEDIMENT WAITING TIME DISTRIBUTIONS

2016 ◽  
Author(s):  
Katherine Skalak ◽  
◽  
James Pizzuto ◽  
Diana Karwan ◽  
Adam Benthem ◽  
...  
Keyword(s):  
Waiting Time ◽  
Age Dating ◽  
Waiting Time Distributions

scholarly journals Waiting time distributions in a two-level fluctuator coupled to a superconducting charge detector

2019 ◽  
Vol 1 (3) ◽  
Author(s):  
Máté Jenei ◽  
Elina Potanina ◽  
Ruichen Zhao ◽  
Kuan Y. Tan ◽  
Alessandro Rossi ◽  
...  
Keyword(s):  
Waiting Time ◽  
Waiting Time Distributions

Earthquakes Descaled: On Waiting Time Distributions and Scaling Laws

2005 ◽  
Vol 94 (10) ◽  
Author(s):  
Mattias Lindman ◽  
Kristin Jonsdottir ◽  
Roland Roberts ◽  
Björn Lund ◽  
Reynir Bödvarsson
Keyword(s):  
Waiting Time ◽  
Scaling Laws ◽  
Waiting Time Distributions

scholarly journals Extended kinetic models with waiting-time distributions: Exact results

2000 ◽  
Vol 113 (24) ◽  
pp. 10867-10877 ◽  
Author(s):  
Anatoly B. Kolomeisky ◽  
Michael E. Fisher
Keyword(s):  
Waiting Time ◽  
Kinetic Models ◽  
Exact Results ◽  
Waiting Time Distributions

On waiting time distributions for patterns in a sequence of multistate trials

2010 ◽  
Vol 80 (23-24) ◽  
pp. 1798-1805
Author(s):  
P.G. Sankaran ◽  
N.N. Midhu
Keyword(s):  
Waiting Time ◽  
Waiting Time Distributions

scholarly journals The waiting time analysis of a discrete-time queue with arrivals as a discrete autoregressive process of order 1

2002 ◽  
Vol 39 (03) ◽  
pp. 619-629 ◽  
Author(s):  
Gang Uk Hwang ◽  
Bong Dae Choi ◽  
Jae-Kyoon Kim
Keyword(s):  
Discrete Time ◽  
Waiting Time ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Autoregressive Process ◽  
Waiting Time Distribution ◽  
Tail Probabilities ◽  
Waiting Time Distributions ◽  
Virtual Waiting Time ◽  
Asymptotic Decay Rate

We consider a discrete-time queueing system with the discrete autoregressive process of order 1 (DAR(1)) as an input process and obtain the actual waiting time distribution and the virtual waiting time distribution. As shown in the analysis, our approach provides a natural numerical algorithm to compute the waiting time distributions, based on the theory of the GI/G/1 queue, and consequently we can easily investigate the effect of the parameters of the DAR(1) on the waiting time distributions. We also derive a simple approximation of the asymptotic decay rate of the tail probabilities for the virtual waiting time in the heavy traffic case.

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