Related papers: Mills' ratio: Reciprocal convexity and functional …
We derive some estimates for the integral modulus of continuity of probability densities of infinitely divisible distributions. The paper is splitted into two parts. The first part deals with general infinitely divisible distributions. The…
This paper develops some objective priors for certain parameters of the bivariate normal distribution. The parameters considered are the regression coefficient, the generalized variance, and the ratio of the conditional variance of one…
In this paper, using inverse integral transforms, we derive the exact distribution of the random variable $X$ that is involved in the ratio $Z \stackrel{d}{=} X/(X+Y)$ where $X$ and $Y$ are independent random variables having the same…
In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent…
We consider composite loss functions for multiclass prediction comprising a proper (i.e., Fisher-consistent) loss over probability distributions and an inverse link function. We establish conditions for their (strong) convexity and explore…
The convex transform order is one way to make precise comparison between the skewness of probability distributions on the real line. We establish a simple and complete characterisation of when one Beta distribution is smaller than another…
In this paper our aim is to present some monotonicity and convexity properties for the one dimensional regularization of the Coulomb potential, which has applications in the study of atoms in magnetic fields and which is in fact a…
An integral over the interval $(0,\pi)$ is given for the cumulative distribution function of a sum of independent gamma random variables with different scale and shape parameters. The cumulative distribution function of a positive definite…
In application areas like bioinformatics multivariate distributions on angles are encountered which show significant clustering. One approach to statistical modelling of such situations is to use mixtures of unimodal distributions. In the…
Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…
Langevin diffusion is a commonly used tool for sampling from a given distribution. In this work, we establish that when the target density $p^*$ is such that $\log p^*$ is $L$ smooth and $m$ strongly convex, discrete Langevin diffusion…
In this paper, the joint distribution of the sum and maximum of independent, not necessarily identically distributed, nonnegative random variables is studied for two cases: i) continuous and ii) discrete random variables. First, a recursive…
In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…
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…
This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the $n$ partitions of the interval $[0,W_n]$ are independent and identically distributed…
In the paper, necessary and sufficient conditions are presented for a function involving a ratio of gamma functions to be logarithmically completely monotonic. This extends and generalizes the main result in [\emph{Inequalities and…
In this paper, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…