Multivariate Bernoulli Distribution Research Articles

Some representations of the multivariate Bernoulli and binomial distributions

Multivariate but vectorized versions for Bernoulli and binomial distributions are established using the concept of Kronecker product from matrix calculus. The multivariate Bernoulli distribution entails a parameterized model, that provides an alternative to the traditional log-linear model for binary variables.

A Note on the attainment of the cramér-rao bound in the sequential case

Under some assumptions, Ghosh (1987) has shown that the Cramer-Rao bound is attained for some strictly sequential procedure if and only if the observations follow the Bernoulli distribution. An extension of this result to the multivariate case via the arguments of Stefanov (1985) is presented. Furthermore, by imposing additional assumptions, we try to find an analogue of the above result of Ghosh in the multivariate case. In the latter case the role of the Bernoulli distribution is performed by the multivariate Bernoulli distribution.

Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials

A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixner–Pollaczek polynomials is presented. It is shown that these are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace. The weight function associated with the Krawtchouk polynomials is the multivariate binomial distribution.

P Value Adjustments for Multiple Tests in Multivariate Binomial Models

Abstract Data from rodent carcinogenicity (preclinical) and clinical studies involving new drugs may be modeled as having come from multivariate binomial distributions. In two-year rodent carcinogenicity studies, there are typically 20–50 tissues examined for occurrence of any of several possible lesions. For a particular treatment group, the number of occurrences of a particular lesion at a particular tissue may be modeled as binomial, and the vector of such frequencies may be considered multivariate binomial with unspecified dependence structure. The same model may also apply to clinical side-effects data; in this case the marginal frequencies may represent occurrences of events ranging from headaches to ingrown toenails. Frequently, the goal of such studies is to isolate site-specific significant differences between treatment and control groups. For example, in rodent carcinogenicity analyses it is generally not sufficient to claim that a new compound causes an increase in tumors at some unspecified si...

On a characterization of the dispersion matrix based on the properties of regression

This paper provides a partial solution to a problem posed by J. Neyman (1965) regarding the characterization of multivariate negative binomial distribution based on the properties of regression. It is shown that some of the properties of regression characterize the form of the nonsingular dispersion matrix of the parent distribution, which, interestingly enough, corresponds to only two types viz. those of positive and negative multivariate binomial distributions.

A Characterization of Multivariate Binomial Distribution by Univariate Marginals1

A distribution P0 of a random vector X = ( X1,..., X n) is said to be linear exponential in a parameter θ = ( θ1,..., θ n) if [Formula: see text]. A multivariate linear exponential distribution is binomial if and only if its univariate marginals are binomial.

PATTERN CLUSTERING BY MULTIVARIATE MIXTURE ANALYSIS.

Cluster analysis is reformulated as a problem of estimating the para- meters of a mixture of multivariate distributions. The maximum-likelihood theory and numerical solution techniques are developed for a fairly general class of distributions. The theory is applied to mixtures of multivariate nor- mals (NORMIX) and mixtures of multivariate Bernoulli distributions (Latent Classes). The feasibility of the procedures is demonstrated by two examples of computer solutions for normal mixture models of the Fisher Iris data and of artifjcially generated clusters with unequal covariance matrices.

定性的な変量による統計的判別理論とその気象への応用

The statistical discrimination theory was first proposed by C. R. Rao (1948) and has been widely applied to the several domains of scientific classification. Its theoretical development has been due to the work of C. R. Rao, S. S. Wilks, J. G. Bryan and others. It was recently applied to meteorological classifactory preciction by R. G. Miller (1962-1964) and by the present author (1963-1965) almost concurrently.In this paper, a simple optimum linear discrimination function is firstly investigated for the case containing several qualitative or categorical variables only, based on the joint probability dis-tribution (i. e., multi-variate binomial distribution) defined by A. S. Krishnamoorthy (1951) and by the author (1966).Secondly the quantification procedure maximizing the correlation ratio between classified predictand variable Y and categorical set of predictor variable X used for classification (of Y), which has already been shown by C. Hayashi and S. Chino, is taken into account through com-bining it with a linear discriminant function.Lastly, several explanatory examples are shown for qualitative prediction of the rain state and the occurrence or non-occurrence of snowslide by using the effective presaged predictors.