Here, T is the time of an event and Z a p-dimensional vector of covariates, φ a square integrable function, and F(t | z) = P (T ≤ t | Z = z) and H( dz) = P (Z ∈ dz) denote the conditional survival distribution and the marginal law of Z , respectively. For example, θ(I {t > t∗}) is the marginal survival probability at time t∗, θ(I {t > t∗, z1 > z∗ 1}) the bivariate distribution at (t∗, z∗ 1) (Ak...

This work shows that a multilayer perceptron can successfully be applied for approximation of conditional probability function. Such an approach makes it possible to examine the training sample with contradictory vectors and to interpret the outputs of the network in classification tasks as the evaluation of the probability of belonging to the specific class. This method was used for creating t...

A probabilistic definition of saliency is given in a form suitable for applications to image matching. In order to make this definition, the values of the pixels in pairs of matching regions are modeled using an elliptically symmetric distribution (ESD). The values of the pixels in background pairs of regions are also modeled using an ESD. If a region is given in one image, then the conditional...

A new family of distributions called Ristic-Balakhrishnan Odd Burr III-G (RBOB III-G) distribution is proposed. We obtain some mathematical and statistical properties this such as hazard reverse hazardfunctions, quantile function, moments generating functions, conditional moments, Rényi entropy, order statistics, stochastic ordering probability weighted moments. The model parameters are estimat...

This paper presents a detailed structural reliability procedure in order to achieve an acceptable safety margin for template type offshore platforms located in the Persian Gulf. Probability of failure in this study is calculated by considering the cumulative effects of all levels of wave loading during the lifetime of the structure and uncertainties associated with soil, material properties, co...

The complexmeasure theoretic approach proposed earlier is reviewed and a general version of density matrix as well as conditional density matrix is introduced. The holomorphic extension of the complex measure density (CMD) is identified to be the Wigner distribution function of the conventional quantum mechanical theory. A variety of situations in quantum optical phenomena are discussed within ...

We consider the optical fiber channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. Using the Feynman path-integral approach for the model, we find corrections to conditional probability density function, output signal distribution, conditional and output signal entropies, and the channel capacity at large signal-to-noise ratio. We demonstrate t...

Abstract: Let X be a Kotz Type III elliptical random vector in IR, k ≥ 2, and let tn, n ≥ 1 be positive constants such that limn→∞ tn = ∞. In this article we obtain an asymptotic expansion of the tail probability P {X > tna},a ∈ IR. As an application we derive an approximation for the conditional excess distribution. Furthermore, we discuss the asymptotic dependence of Kotz Type III triangular ...