Fractional statistic

We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes sense for finite $N=pm+r$ with $p$ integer and $0<r\leq m.$ A geometrical interpretation of fractional statistic is given in terms of ''composite particles''.Comment: flatex hald.tex, 3 files Submitted to: Phys. Rev.

Statistic Rate Monotonic Scheduling

In this paper we present Statistical Rate Monotonic Scheduling (SRMS), a generalization of the classical RMS results of Liu and Layland that allows scheduling periodic tasks with highly variable execution times and statistical QoS requirements. Similar to RMS, SRMS has two components: a feasibility test and a scheduling algorithm. The feasibility test for SRMS ensures that using SRMS' scheduling algorithms, it is possible for a given periodic task set to share a given resource (e.g. a processor, communication medium, switching device, etc.) in such a way that such sharing does not result in the violation of any of the periodic tasks QoS constraints. The SRMS scheduling algorithm incorporates a number of unique features. First, it allows for fixed priority scheduling that keeps the tasks' value (or importance) independent of their periods. Second, it allows for job admission control, which allows the rejection of jobs that are not guaranteed to finish by their deadlines as soon as they are released, thus enabling the system to take necessary compensating actions. Also, admission control allows the preservation of resources since no time is spent on jobs that will miss their deadlines anyway. Third, SRMS integrates reservation-based and best-effort resource scheduling seamlessly. Reservation-based scheduling ensures the delivery of the minimal requested QoS; best-effort scheduling ensures that unused, reserved bandwidth is not wasted, but rather used to improve QoS further. Fourth, SRMS allows a system to deal gracefully with overload conditions by ensuring a fair deterioration in QoS across all tasks---as opposed to penalizing tasks with longer periods, for example. Finally, SRMS has the added advantage that its schedulability test is simple and its scheduling algorithm has a constant overhead in the sense that the complexity of the scheduler is not dependent on the number of the tasks in the system. We have evaluated SRMS against a number of alternative scheduling algorithms suggested in the literature (e.g. RMS and slack stealing), as well as refinements thereof, which we describe in this paper. Consistently throughout our experiments, SRMS provided the best performance. In addition, to evaluate the optimality of SRMS, we have compared it to an inefficient, yet optimal scheduler for task sets with harmonic periods.National Science Foundation (CCR-970668

The Bayesian Score Statistic

We propose a novel Bayesian test under a (noninformative) Jeffreys’ prior speciï¬ca- tion. We check whether the ï¬xed scalar value of the so-called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standard- ized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothe- sis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys’ priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspeciï¬cation in linear and cointegration models.bayesian statistics

The Bayesian Score Statistic

We propose a novel Bayesian test under a (noninformative) Jeffreys' prior specification. We check whether the fixed scalar value of the so- called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standardized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothesis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys' priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspecification in linear and cointegration models.

Sondajul statistic în turism

The statistical survey has a broad area of application in the sphere of tourism. It represents the statistical method of establishment, based on the sampler, on the opinions of different socio-professional categories, with the purpose of anticipating the behavior of the collectivity’s members. The essential idea of the survey is that, at the basis of every person’s opinions and behavior, stands a general system of references and meanings. Therefore, the individual, subjective opinions present an objective significance that can be generalized and measured. The survey can be applied in the study of the touristical demand, in the researches that are made in order to get to know the tourists’ requests and motivations.Statistical survey, stratified survey, questionnaire,

The seasonal KPSS statistic

In this paper a seasonal version of the KPSS test for unit roots are proposed and its asymptotic distribution is stated. Further, a small Monte Carlo simulation is used to analyse some size and power properties.