Search results for "Univariate distribution"
showing 5 items of 5 documents
An alternative representation of Altham's multiplicative-binomial distribution
1998
Abstract Cox (1972) introduced a log-linear representation for the joint distribution of n binary-dependent responses. Altham (1978) derived the distribution of the sum of such responses, under a multiplicative, rather than log-linear, representation and called it multiplicative-binomial. We propose here an alternative form of the multiplicative-binomial, which is derived from the original Cox's representation and is characterized by intuitively meaningful parameters, and compare its first two moments with those of the standard binomial distribution.
Efficient Simulation of Multivariate Binomial and Poisson Distributions
1998
Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the mult…
Multivariate exponential smoothing: A Bayesian forecast approach based on simulation
2009
This paper deals with the prediction of time series with correlated errors at each time point using a Bayesian forecast approach based on the multivariate Holt-Winters model. Assuming that each of the univariate time series comes from the univariate Holt-Winters model, all of them sharing a common structure, the multivariate Holt-Winters model can be formulated as a traditional multivariate regression model. This formulation facilitates obtaining the posterior distribution of the model parameters, which is not analytically tractable: simulation is needed. An acceptance sampling procedure is used in order to obtain a sample from this posterior distribution. Using Monte Carlo integration the …
Stochastic discretized learning-based weak estimation: a novel estimation method for non-stationary environments
2016
The task of designing estimators that are able to track time-varying distributions has found promising applications in many real-life problems.Existing approaches resort to sliding windows that track changes by discarding old observations. In this paper, we report a novel estimator referred to as the Stochastic Discretized Weak Estimator (SDWE), that is based on the principles of discretized Learning Automata (LA). In brief, the estimator is able to estimate the parameters of a time varying binomial distribution using finite memory. The estimator tracks changes in the distribution by operating a controlled random walk in a discretized probability space. The steps of the estimator are discre…
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…