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.

A scale-free adaptive statistic for testing exponentiality against Weibull and generalized Pareto distributions

In Fortiana and Grané (2002) we study a scale-free statistic, based on Hoeffding's maximum correlation, for testing exponentiality. This statistic admits an expansion along a countable set of orthogonal axes, originating a sequence of statistics. Linear combinations of a given number p of terms in this sequence can be written as a quotient of L-statistics. In this paper we propose a scalefree adaptive statistic for testing exponentiality with optimal power against a specific alternative. We obtain its exact distribution and compare it with other scale-free statistics for testing exponentiality, such as the Stephens' modification of the Shapiro-Wilk statistic, the Gini statistic and the Qn statistic defined in Fortiana and Grané (2002)

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 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