Mean recurrence times for k successes within m trials

1976 ◽  
Vol 13 (03) ◽  
pp. 604-607 ◽  
Author(s):  
Raymond J. Huntington
Keyword(s):  
Recurrent Event ◽  
Recurrence Time ◽  
Bernoulli Trials ◽  
Closed Expression ◽  
Recurrence Times ◽  
The Mean

Given an unlimited sequence of Bernoulli trials, let E be the recurrent event that k or more successes occur within m consecutive trials in the sequence. Let μk, m denote the mean recurrence time for E. Previous work finds expressions for μk, m for limited values of k and m. The present paper derives a closed expression for μk, m for all k, m. Tables for μk, m are also presented.

Mean recurrence times for k successes within m trials

1976 ◽  
Vol 13 (3) ◽  
pp. 604-607 ◽  
Author(s):  
Raymond J. Huntington
Keyword(s):  
Recurrent Event ◽  
Recurrence Time ◽  
Bernoulli Trials ◽  
Closed Expression ◽  
Recurrence Times ◽  
The Mean

Given an unlimited sequence of Bernoulli trials, let E be the recurrent event that k or more successes occur within m consecutive trials in the sequence. Let μk, m denote the mean recurrence time for E. Previous work finds expressions for μk, m for limited values of k and m. The present paper derives a closed expression for μk, m for all k, m. Tables for μk, m are also presented.

Recurrence times of draft-patterns from reservoirs

1975 ◽  
Vol 12 (03) ◽  
pp. 647-652 ◽  
Author(s):  
G. G. S. Pegram
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Recurrence Time ◽  
Reservoir Model ◽  
Discrete State ◽  
Discrete Time Markov Chain ◽  
Recurrence Times ◽  
Mean And Variance ◽  
The Mean ◽  
Run Theory

Expressions for the mean and variance of the recurrence time of non-overlapping draft-patterns of draft from a Moran Reservoir Model (discrete-state and discrete-time Markov chain) are derived using Feller's Renewal argument. In addition an expression for the mean recurrence time for self-overlapping patterns of draft is derived using run-theory.

scholarly journals Standard deviation of recurrence times for piecewise linear transformations

2017 ◽  
Vol 10 (01) ◽  
pp. 1750009
Author(s):  
Mimoon Ismael ◽  
Rodney Nillsen ◽  
Graham Williams
Keyword(s):  
Standard Deviation ◽  
Dynamical Systems ◽  
Piecewise Linear ◽  
Recurrence Formula ◽  
Recurrence Time ◽  
Linear Transformations ◽  
Recurrence Times ◽  
Borel Set ◽  
Bounded Interval ◽  
The Mean

This paper is concerned with dynamical systems of the form [Formula: see text], where [Formula: see text] is a bounded interval and [Formula: see text] comes from a class of measure-preserving, piecewise linear transformations on [Formula: see text]. If [Formula: see text] is a Borel set and [Formula: see text], the Poincaré recurrence time of [Formula: see text] relative to [Formula: see text] is defined to be the minimum of [Formula: see text], if the minimum exists, and [Formula: see text] otherwise. The mean of the recurrence time is finite and is given by Kac’s recurrence formula. In general, the standard deviation of the recurrence times need not be finite but, for the systems considered here, a bound for the standard deviation is derived.

Recurrence times of draft-patterns from reservoirs

1975 ◽  
Vol 12 (3) ◽  
pp. 647-652 ◽  
Author(s):  
G. G. S. Pegram
Keyword(s):  
Markov Chain ◽  
Discrete Time ◽  
Recurrence Time ◽  
Reservoir Model ◽  
Discrete State ◽  
Discrete Time Markov Chain ◽  
Recurrence Times ◽  
Mean And Variance ◽  
The Mean ◽  
Run Theory

Expressions for the mean and variance of the recurrence time of non-overlapping draft-patterns of draft from a Moran Reservoir Model (discrete-state and discrete-time Markov chain) are derived using Feller's Renewal argument. In addition an expression for the mean recurrence time for self-overlapping patterns of draft is derived using run-theory.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

Bounds on the mean recurrence time of subclinical epidemics in dairy herds

1967 ◽  
Vol 17 (1) ◽  
pp. 47-56 ◽  
Author(s):  
D.S. Robson ◽  
R.F. Kahrs ◽  
J.A. Baker
Keyword(s):  
Recurrence Time ◽  
Dairy Herds ◽  
The Mean

A Theoretical Framework for Estimating Swarm Success Probability Using Scouts

2010 ◽  
Vol 1 (4) ◽  
pp. 17-45
Author(s):  
Antons Rebguns ◽  
Diana F. Spears ◽  
Richard Anderson-Sprecher ◽  
Aleksey Kletsov
Keyword(s):  
Mean Squared Error ◽  
Success Probability ◽  
Ground Truth ◽  
Theoretical Framework ◽  
Bernoulli Trials ◽  
Lennard Jones ◽  
Squared Error ◽  
The Mean ◽  
The Bayesian Approach ◽  
Bayesian Formula

This paper presents a novel theoretical framework for swarms of agents. Before deploying a swarm for a task, it is advantageous to predict whether a desired percentage of the swarm will succeed. The authors present a framework that uses a small group of expendable “scout” agents to predict the success probability of the entire swarm, thereby preventing many agent losses. The scouts apply one of two formulas to predict – the standard Bernoulli trials formula or the new Bayesian formula. For experimental evaluation, the framework is applied to simulated agents navigating around obstacles to reach a goal location. Extensive experimental results compare the mean-squared error of the predictions of both formulas with ground truth, under varying circumstances. Results indicate the accuracy and robustness of the Bayesian approach. The framework also yields an intriguing result, namely, that both formulas usually predict better in the presence of (Lennard-Jones) inter-agent forces than when their independence assumptions hold.

Some renewal process models for single neuron discharge

1971 ◽  
Vol 8 (4) ◽  
pp. 802-808 ◽  
Author(s):  
Howard G. Hochman ◽  
Stephen E. Fienberg
Keyword(s):  
Single Neuron ◽  
Interspike Interval ◽  
Poisson Processes ◽  
Process Models ◽  
Recurrence Time ◽  
The Laplace Transform ◽  
Mean And Variance ◽  
The Mean ◽  
Interspike Interval Distribution ◽  
Interval Distribution

Leslie (1969) obtained the Laplace transform for the recurrence time of clusters of Poisson processes, which can be thought of as yielding the interspike interval distribution for a neuron that receives Poisson excitatory inputs subject to decay. Here, several extensions of this model are derived, each including Poisson inhibitory inputs. Expressions for the mean and variance are derived for each model, and the results for the different models are compared.

Poisson recurrence times

1967 ◽  
Vol 4 (03) ◽  
pp. 605-608
Author(s):  
Meyer Dwass
Keyword(s):  
Random Walk ◽  
Waiting Time ◽  
Waiting Times ◽  
Random Variables ◽  
Recurrent Event ◽  
Recurrence Times ◽  
Image Position ◽  
Independent And Identically Distributed

Let Y1, Y 2, … be a sequence of independent and identically distributed Poisson random variables with parameter λ. Let Sn = Y 1 + … + Yn, n = 1,2,…, S 0 = 0. The event Sn = n is a recurrent event in the sense that successive waiting times between recurrences form a sequence of independent and identically distributed random variables. Specifically, the waiting time probabilities are (Alternately, the fn can be described as the probabilities for first return to the origin of the random walk whose successive steps are Y1 − 1, Y2 − 1, ….)

scholarly journals A Generalized Telegraph Process with Velocity Driven by Random Trials

2013 ◽  
Vol 45 (04) ◽  
pp. 1111-1136 ◽  
Author(s):  
Irene Crimaldi ◽  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci
Keyword(s):  
Real Line ◽  
Counting Process ◽  
Bernoulli Trials ◽  
Exponential Distributions ◽  
The Real ◽  
Telegraph Process ◽  
Nonzero Mean ◽  
The Mean ◽  
Moving Particle ◽  
Random Trial

We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

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