Related papers: Mills' ratio: Reciprocal convexity and functional …
Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
Probability distributions defined on the unit interval are widely used in fields ranging from econometrics to reliability studies. Traditional models such as the beta and Kumaraswamy distributions are well-established due to their…
Posterior predictive p-values are a common approach to Bayesian model-checking. This article analyses their frequency behaviour, that is, their distribution when the parameters and the data are drawn from the prior and the model…
In this article, we employ a standard convex argument to obtain new and refined inequalities related to the matrix mean of two accretive matrices, the numerical radius and the Tsallis relative operator entropy.
In information theory, some optimization problems result in convex optimization problems on strictly convex functionals of probability densities. In this note, we study these problems and show conditions of minimizers and the uniqueness of…
The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes SP_{p}({\alpha},\b{eta}) and UCV_{p}({\alpha},\b{eta}) of uniformly spirallike functions.…
A test of the concavity of a distribution function with support contained in the unit interval may be based on a statistic constructed from the $L^p$-norm of the difference between an empirical distribution function and its least concave…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
We consider the problem of estimating the joint distribution of a continuous-time perpetuity and the underlying factors which govern the cash flow rate, in an ergodic Markov model. Two approaches are used to obtain the distribution. The…
We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…
Recent literature in the last Maximum Entropy workshop introduced an analogy between cumulative probability distributions and normalized utility functions. Based on this analogy, a utility density function can de defined as the derivative…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
Quantum field model of unstable particles with random mass is suggested to describe the finite-width effects in decay rate. Within the framework of this model we derive the convolution formula for a width of the channels with unstable…
Gram's Law describes a pattern that frequently occurs in the distribution of the non-trivial zeros of the Riemann zeta function along the critical line. Whenever Gram's Law holds true, it reduces the difficulty of computing the…
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.
The constitutive modelling of granular, porous and quasi-brittle materials is based on yield (or damage) functions, which may exhibit features (for instance, lack of convexity, or branches where the values go to infinity, or false elastic…