Search results for "Normal"
showing 10 items of 2571 documents
A matrix-valued Bernoulli distribution
2006
AbstractMatrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.
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…
Adaptive designs with correlated test statistics
2009
In clinical trials, the collected observations such as clustered data or repeated measurements are often correlated. As a consequence, test statistics in a multistage design are correlated. Adaptive designs were originally developed for independent test statistics. We present a general framework for two-stage adaptive designs with correlated test statistics. We show that the significance level for the Bauer-Köhne design is inflated for positively correlated test statistics from a bivariate normal distribution. The decision boundary for the second stage can be modified so that type one error is controlled. This general concept is expandable to other adaptive designs. In order to use these de…
Tests of Linearity, Multivariate Normality and the Adequacy of Linear Scores
1994
After some discussion of the purposes of testing multivariate normality, the paper concentrates on two different approaches to testing linearity: on repeated regression tests of non-linearity and on exploiting properties of a dichotomized normal distribution. Regression tests of linearity are used to examine the adequacy of linear scoring systems for explanatory variables, initially recorded on an ordinal scale. Examples from recent psychological and medical research are given in which the methods have led to some insight into subject-matter.
On (n-l)-wise and joint independence and normality of n Random variables: an example
1981
An example is given of a vector of n random variables such that any (n-1)-dimensional subvector consists of n-1 independent standard normal variables. The whole vector however is neither independent nor normal.
Critical phenomena at surfaces
1990
Abstract The presence of free surfaces adds a rich and interesting complexity to critical phenomena associated with phase transitions occurring in bulk materials. We shall review Monte Carlo computer simulation studies of surface critical behavior in simple cubic Ising- and XY-models with nearest-neighbor interactions J in the bulk and Js at the surface. These studies allow the identification of various critical exponents and critical amplitude ratios involving both the critical behavior of local quantities and of surface excess corrections to the bulk. We consider both the “ordinary” transition (surface criticality controlled by the bulk) and the “special transition” (a multicritical point…
Fisher Renormalization for Logarithmic Corrections
2008
For continuous phase transitions characterized by power-law divergences, Fisher renormalization prescribes how to obtain the critical exponents for a system under constraint from their ideal counterparts. In statistical mechanics, such ideal behaviour at phase transitions is frequently modified by multiplicative logarithmic corrections. Here, Fisher renormalization for the exponents of these logarithms is developed in a general manner. As for the leading exponents, Fisher renormalization at the logarithmic level is seen to be involutory and the renormalized exponents obey the same scaling relations as their ideal analogs. The scheme is tested in lattice animals and the Yang-Lee problem at t…
Phase Transitions in the Multicomponent Widom-Rowlinson Model and in Hard Cubes on the BCC--Lattice
1997
We use Monte Carlo techniques and analytical methods to study the phase diagram of the M--component Widom-Rowlinson model on the bcc-lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M greater or equal 3 there is a ``crystal phase'' for z lying between z_c(M) and z_d(M) while for z > z_d(M) there are M demixed phases each consisting mostly of one species. For M=2 there is a direct second order transition from the gas phase to the demixed phase while for M greater or equal 3 the transition at z_d(M) appears to be first order putting it in the Potts model universality class. For M large, …
Monte Carlo investigations of phase transitions: status and perspectives
2000
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies of Ising models are discussed, as well as the extension to models of polymer mixtures and solutions. It is shown that using appropriate cluster algorithms, even the scaling functions describing the crossover from the Ising universality class to the mean-field behavior with increasing interaction range can be described. Additionally, the issue of finite-size scaling in Ising models above the marginal dimension (d*=4) is discussed.
Some results on the rotated infinitely deep potential and its coherent states
2021
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, he…