The article presents conditions under which the probability of a linear combination random vectors falling into polyhedral cone is Schur-concave function coefficients combination. It required that contains point 0, its edges are parallel to coordinate axes, and distribution density logarithmically concave sign-invariant function.

The Compact Genetic Algorithm (cGA) has a distinct characteristic that it requires almost minimal memory to store candidate solutions. The probability vector is used to generate candidate solutions. This probability vector represents a structure of the population as a probability distribution over the set of solution. It has been established that the power of cGA is comparable to the standard S...

Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...

A fault detection and isolation (FDI) problem is considered for inertial sensors, such as gyroscopes and accelerometers and a new FDI method for double faults is proposed using reduced-order parity vector. The reduced-order parity vector (RPV) algorithm enables us to isolate double faults with 7 sensors. Averaged parity vector is used to reduce false alarm and wrong isolation, and to improve co...

Support vector machines have attracted much attention in theoretical and in applied statistics. Main topics of recent interest are consistency, learning rates and robustness. In this article, it is shown that support vector machines are qualitatively robust. Since support vector machines can be represented by a functional on the set of all probability measures, qualitative robustness is proven ...

How to extend standard support vector machines to solve multi-class classification problem and yield the outputs in the frame of Dempster-Shafer theory is useful. The multi-class probability support vector machine is proposed, firstly. The Dempster-Shafer theory based multi-class support vector machine is designed by constructing probability support vector machines for binary classification usi...

Hidden Markov Models have been proved to be an efficient way for statistically modeling sequence signals. And the Support Vector Machines seem to be a promising candidate to perform the classification task. A new method combining support vector machine and hidden Markov models is proposed. The output of support vector machines are modified as posterior probability using sigmoid function, and ac...

In this paper we propose and develop an iterative method to calculate a limiting probability distribution vector of a transition probability tensor P arising from a higher-order Markov chain. In the model, the computation of such limiting probability distribution vector x can be formulated as a Z-eigenvalue problem Pxm−1 = x associated with the eigenvalue 1 of P where all the entries of x are r...