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A survey on continuous elliptical vector distributions.

Eusebio Gómez, Miguel A. Gómez-Villegas, J. Miguel Marín (2003)

Revista Matemática Complutense

In this paper it is taken up a revision and characterization of the class of absolutely continuous elliptical distributions upon a parameterization based on the density function. Their properties (probabilistic characteristics, affine transformations, marginal and conditional distributions and regression) are shown in a practical and easy to interpret way. Two examples are fully undertaken: the multivariate double exponential distribution and the multivariate uniform distribution.

A theoretical comparison of disco and CADIAG-II-like systems for medical diagnoses

Tatiana Kiseliova (2006)

Kybernetika

In this paper a fuzzy relation-based framework is shown to be suitable to describe not only knowledge-based medical systems, explicitly using fuzzy approaches, but other ways of knowledge representation and processing. A particular example, the practically tested medical expert system Disco, is investigated from this point of view. The system is described in the fuzzy relation-based framework and compared with CADIAG-II-like systems that are a “pattern” for computer-assisted diagnosis systems based...

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...

A two-disorder detection problem

Krzysztof Szajowski (1997)

Applicationes Mathematicae

Suppose that the process X = { X n , n } is observed sequentially. There are two random moments of time θ 1 and θ 2 , independent of X, and X is a Markov process given θ 1 and θ 2 . The transition probabilities of X change for the first time at time θ 1 and for the second time at time θ 2 . Our objective is to find a strategy which immediately detects the distribution changes with maximal probability based on observation of X. The corresponding problem of double optimal stopping is constructed. The optimal strategy is found...

A unified terminology in block designs

Tadeusz Caliński, Sanpei Kageyama (2004)

Discussiones Mathematicae Probability and Statistics

Partially efficiency balanced (PEB) designs with m efficiency classes have been defined by Puri and Nigam [15] as block designs which have simple analysis and, if properly used, allow the important contrasts to be estimated with desired efficiency. Such designs can be made available in varying replications and/or unequal block sizes. However, any block design is a PEB design with m efficiency classes for some m < v, where v is the number of treatments in the design. So the term "PEB" itself is...

A uniform central limit theorem for dependent variables

Konrad Furmańczyk (2009)

Applicationes Mathematicae

Niemiro and Zieliński (2007) have recently obtained uniform asymptotic normality for the Bernoulli scheme. This paper concerns a similar problem. We show the uniform central limit theorem for a sequence of stationary random variables.

A variant of gravitational classification

Tomasz Górecki, Maciej Luczak (2014)

Biometrical Letters

In this article there is proposed a new two-parametrical variant of the gravitational classification method. We use the general idea of objects' behavior in a gravity field. Classification depends on a test object's motion in a gravity field of training points. To solve this motion problem, we use a simulation method. This classifier is compared to the 1NN method, because our method tends towards it for some parameter values. Experimental results on different data sets demonstrate an improvement...

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