92 research outputs found
Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
We investigate the non-ergodic properties of blinking nano-crystals using a
stochastic approach. We calculate the distribution functions of the time
averaged intensity correlation function and show that these distributions are
not delta peaked on the ensemble average correlation function values; instead
they are W or U shaped. Beyond blinking nano-crystals our results describe
non-ergodicity in systems stochastically modeled using the Levy walk framework
for anomalous diffusion, for example certain types of chaotic dynamics,
currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure
Optimal design of measurements on queueing systems
We examine the optimal design of measurements on queues with particular reference to the M/M/1 queue. Using the statistical theory of design of experiments, we calculate numerically the Fisher information matrix for an estimator of the arrival rate and the service rate to find optimal times to measure the queue when the number of measurements are limited for both interfering and non-interfering measurements. We prove that in the non-interfering case, the optimal design is equally spaced. For the interfering case, optimal designs are not necessarily equally spaced. We compute optimal designs for a variety of queuing situations and give results obtained under the - and -optimality criteria
Limiting distributions for explosive PAR(1) time series with strongly mixing innovation
This work deals with the limiting distribution of the least squares
estimators of the coefficients a r of an explosive periodic autoregressive of
order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k }
is strongly mixing. More precisely {a r } is a periodic sequence of real
numbers with period P \textgreater{} 0 and such that P r=1 |a r |
\textgreater{} 1. The time series {u r } is periodically distributed with the
same period P and satisfies the strong mixing property, so the random variables
u r can be correlated
A Powerful Test of the Autoregressive Unit Root Hypothesis Based on a Tuning Parameter Free Statistic
Estimation for a class of generalized state-space time series models
State-space models with exponential and conjugate exponential family densities are introduced. Examples include Poisson-Gamma, Binomial-Beta, Gamma-Gamma and Normal-Normal processes. Maximum likelihood and quasilikelihood estimators and their properties are discussed. Results from a simulation study for the Poisson-Gamma model are reported.State-space models Exponential families Conjugate exponential families Maximum likelihood estimation Quasilikelihood estimation
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