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A short note on Perez’s approximation by dependence structure simplification

Radim Jiroušek (2007)

Kybernetika

Perez’s approximations of probability distributions by dependence structure simplification were introduced in 1970s, much earlier than graphical Markov models. In this paper we will recall these Perez’s models, formalize the notion of a compatible system of elementary simplifications and show the necessary and sufficient conditions a system must fulfill to be compatible. For this we will utilize the apparatus of compositional models.

A study of the tangent space model of the von Mises-Fisher distrubution.

A. Chakak, L. Imhali (2003)

RACSAM

For a random rotation X = M0 eφ(ε) where M0 is a 3 x 3 rotation, ε is a trivariate random vector, and φ(ε) is a skew symmetric matrix, the least squares criterion consists of seeking a rotation M called the mean rotation minimizing tr[(M - E(X))t (M - E(X))]. Some conditions on the distribution of ε are set so that the least squares estimator is unbiased. Of interest is when ε is normally distributed N(0;Σ). Unbiasedness of the least squares estimator is dealt with according to eigenvalues of Σ.

A theory for non-linear prediction approach in the presence of vague variables: with application to BMI monitoring

R. Pourmousa, M. Rezapour, M. Mashinchi (2015)

Dependence Modeling

In the statistical literature, truncated distributions can be used for modeling real data. Due to error of measurement in truncated continuous data, choosing a crisp trimmed point caucuses a fault inference, so using fuzzy sets to define a threshold pointmay leads us more efficient results with respect to crisp thresholds. Arellano-Valle et al. [2] defined a selection distribution for analysis of truncated data with crisp threshold. In this paper, we define fuzzy multivariate selection distribution...

Affinity between complex distribution functions.

Antonio Dorival Campos (1987)

Trabajos de Estadística

By analogy to the real case established by Matusita (1955) we introduce the concept of affinity between two complex distribution functions. We also establish a concrete expression for the affinity between two complex k-variate normal distributions when the covariance matrices assume a special form. Generalizations of these results are presented and the expressions here obtained are compared with those obtained by Matusita (1966, 1967) relative to the affinity between real k-variate normal distributions....

An Approach to Distribution of the Product of Two Normal Variables

Antonio Seijas-Macías, Amílcar Oliveira (2012)

Discussiones Mathematicae Probability and Statistics

The distribution of product of two normally distributed variables come from the first part of the XX Century. First works about this issue were [1] and [2] showed that under certain conditions the product could be considered as a normally distributed. A more recent approach is [3] that studied approximation to density function of the product using three methods: numerical integration, Monte Carlo simulation and analytical approximation to the result using the normal distribution....

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