79 research outputs found
Limiting search cost distribution for the move-to-front rule with random request probabilities
Consider a list of files whose popularities are random. These files are
updated according to the move-to-front rule and we consider the induced Markov
chain at equilibrium. We give the exact limiting distribution of the
search-cost per item as tends to infinity. Some examples are supplied.Comment: move-to-front, search cost, random discrete distribution, limiting
distribution, size biased permutatio
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or popularities). The induced Markov chain is known to be ergodic. One main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers of Barrera and Paroissin and Lijoi and Pruenster that both extend results proved by Kingman on the expected stationary search cost. Combining results contained in these papers, we obtain the limiting behavior for any moments of the stationary seach cost as n tends to infinity.Normalized random measure, Random discrete distribution, Stable subordinator, Problem of heaps
Limiting behavior of the search cost distribution for the move-to-front rule in the stable case
Move-to-front rule is a heuristic updating a list of n items according to requests. Items are required with unknown probabilities (or ppopularities). The induced Markov chain is known to be ergodic [4]. One main problem is the study of the distribution of the search cost defined as the position of the required item. Here we first establish the link between two recent papers [3, 8] that both extend results proved by Kingman [7] on the expected stationary search cost. Combining results contained in these papers, we obtain the limiting behavior for any moments of the stationary seach cost as n tends to infinity.normalized random measure; random discrete distribution; stable subordinator; problem of heaps
A comparison of statistical models for short categorical or ordinal time series with applications in ecology
We study two statistical models for short-length categorical (or ordinal)
time series. The first one is a regression model based on generalized linear
model. The second one is a parametrized Markovian model, particularizing the
discrete autoregressive model to the case of categorical data. These models are
used to analyze two data-sets: annual larch cone production and weekly
planktonic abundance.Comment: 18 page
Joint signature of two or more systems with applications to multistate systems made up of two-state components
The structure signature of a system made up of components having
continuous and i.i.d. lifetimes was defined in the eighties by Samaniego as the
-tuple whose -th coordinate is the probability that the -th component
failure causes the system to fail. More recently, a bivariate version of this
concept was considered as follows. The joint structure signature of a pair of
systems built on a common set of components having continuous and i.i.d.
lifetimes is a square matrix of order whose -entry is the
probability that the -th failure causes the first system to fail and the
-th failure causes the second system to fail. This concept was successfully
used to derive a signature-based decomposition of the joint reliability of the
two systems. In the first part of this paper we provide an explicit formula to
compute the joint structure signature of two or more systems and extend this
formula to the general non-i.i.d. case, assuming only that the distribution of
the component lifetimes has no ties. We also provide and discuss a necessary
and sufficient condition on this distribution for the joint reliability of the
systems to have a signature-based decomposition. In the second part of this
paper we show how our results can be efficiently applied to the investigation
of the reliability and signature of multistate systems made up of two-state
components. The key observation is that the structure function of such a
multistate system can always be additively decomposed into a sum of classical
structure functions. Considering a multistate system then reduces to
considering simultaneously several two-state systems
Passage times of perturbed subordinators with application to reliability
We consider a wide class of increasing Lévy processes perturbed by an independent Brownian motion as a degradation model. Such family contains almost all classical degradation models considered in the literature. Classically failure time associated to such model is defined as the hitting time or the first-passage time of a fixed level. Since sample paths are not in general increasing, we consider also the last-passage time as the failure time following a recent work by Barker and Newby. We address here the problem of determining the distribution of the first-passage time and of the last-passage time. In the last section we consider a maintenance policy for such models
A new non-parametric estimator of the cumulative distribution function under time-and random-censoring
In this paper, we first provide a review of different non-parametric
estimators for the cumulative distribution function under left-censoring. We
then propose a new estimator based on a non-parametric likelihood approach
using reversed hazard rate. Finally, we conclude with an application to a real
data
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