相关论文: On the Generalized Arcsine Probability Distributio…
The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
The normalized incomplete beta function can be defined either as cumulative distribution function of beta density or as the Gauss hypergeometric function with one of the upper parameters equal to unity. Logarithmic concavity/convexity of…
In this paper, we determine necessary and sufficient conditions for the generalized Bessel function to be in certain subclasses of starlike and convex functions. Also, we obtain several corollaries as special cases of the main results,…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…
It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
This paper generalizes the traditional statistical concept of prediction intervals for arbitrary probability density functions in high-dimensional feature spaces by introducing significance level distributions, which provides…
We consider Gibbs distributions, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval…
Optimization is widely used in statistics, and often efficiently delivers point estimates on useful spaces involving structural constraints or combinatorial structure. To quantify uncertainty, Gibbs posterior exponentiates the negative loss…
In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available…
A new family of Barnes beta distributions on $(0, \infty)$ is introduced and its infinite divisibility, moment determinacy, scaling, and factorization properties are established. The Morris integral probability distribution is constructed…
There is given a method for estimation of a probability distribution tail in terms of characteristic function. Key words: characteristic function; tail of a distribution.