Search results for "table"
showing 10 items of 2807 documents
Regression models for multivariate ordered responses via the Plackett distribution
2008
AbstractWe investigate the properties of a class of discrete multivariate distributions whose univariate marginals have ordered categories, all the bivariate marginals, like in the Plackett distribution, have log-odds ratios which do not depend on cut points and all higher-order interactions are constrained to 0. We show that this class of distributions may be interpreted as a discretized version of a multivariate continuous distribution having univariate logistic marginals. Convenient features of this class relative to the class of ordered probit models (the discretized version of the multivariate normal) are highlighted. Relevant properties of this distribution like quadratic log-linear e…
New trends in nonequilibrium statistical mechanics: classical and quantum systems
2020
The main aim of this special issue is to report recent advances and new trends in nonequilibrium statistical mechanics of classical and quantum systems, from both theoretical and experimental points of view, within an interdisciplinary context. In particular, the nonlinear relaxation processes in the dynamics of out-of-equilibrium systems and the role of the metastability and environmental noise will be overviewed. Three main areas of nonequilibrium statistical mechanics will be covered: slow relaxation phenomena and dissipative dynamics; long-range interactions and classical systems; quantum systems. New trends such as quantum thermodynamics and novel types of quantum phase transitions occ…
Affine equivariant multivariate rank methods
2003
The classical multivariate statistical methods (MANOVA, principal component analysis, multivariate multiple regression, canonical correlation, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations. In the paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. Affine equivariant multivariate rank concept is based on the multivariate Oja (Statist. Probab. …
Variable Length Memory Chains: Characterization of stationary probability measures
2021
Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability theory. The question of the existence of stationary probability measures leads us to introduce a key combinatorial structure for words produced by a VLMC: the Longest Internal Suffix. This notion allows us to state a necessary and sufficient condition for a general VLMC to admit a unique invariant probability measure. This condition turns out to get a much simpler form for a subclass of VLMC: the stable VLMC. This natural subclass, unlike the general case, enj…
Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates
2021
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subodinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in Di Crescenzo A., Macci C., Martinucci B. (2014).
Modelling residuals dependence in dynamic life tables: A geostatistical approach
2008
The problem of modelling dynamic mortality tables is considered. In this context, the influence of age on data graduation needs to be properly assessed through a dynamic model, as mortality progresses over the years. After detrending the raw data, the residuals dependence structure is analysed, by considering them as a realisation of a homogeneous Gaussian random field defined on R × R. This setting allows for the implementation of geostatistical techniques for the estimation of the dependence and further interpolation in the domain of interest. In particular, a complex form of interaction between age and time is considered, by taking into account a zonally anisotropic component embedded in…
A comparison of nonparametric methods in the graduation of mortality: Application to data from the Valencia Region (Spain)
2006
[EN] The nonparametric graduation of mortality data aims to estimate death rates by carrying out a smoothing of the crude rates obtained directly from original data. The main difference with regard to parametric models is that the assumption of an age-dependent function is unnecessary, which is advantageous when the information behind the model is unknown, as one cause of error is often the choice of an inappropriate model. This paper reviews the various alternatives and presents their application to mortality data from the Valencia Region, Spain. The comparison leads us to the conclusion that the best model is a smoothing by means of Generalised Additive Models (GAM) with splines. The most…
Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials
2004
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first-passage time (MFPT) as a function of the potential parameters, the noise intensity and the mean rate of switchings of the dichotomous noise. We find noise enhanced stability (NES) phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed. For the diffusion of the overdamped Brownian particle in a fast fluctuating symmetric periodic potential w…
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
2019
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…
13C and15N NMR chemical shift assignments ofN-1-(2- azidoethyl)-4-R-pyrimidin-2-ones by1H,X HMQ(B)C withz-gradient selection
1998
13C and 15N NMR chemical shift assignments based on z-gradient selected 1H,X (X=13C and 15N) HMQC and HMBC experiments are reported for N-1-(2-azidoethyl)pyrimidin-2-one (ring system of cytosine), its five 4-R derivatives [where R=NH2, OCH3, N(CH2)4, NHCH2CH(CH3)2 and N(CH3)2] and 2-azidoethyl tosylate. The possibilities of detecting all nitrogens in these molecules containing (i) an azido group at N-1 and (ii) an electronegative substituent at C-4 are limited. First, the terminal nitrogen of the azido group is difficult to observe because the nearest proton (in a CH2 group) is located four bonds away from it. Second, in contrast to N-1, N-3 in N-1-(2-azido-ethyl)-4-pyrimidin-2-ones remaine…