Related papers: The Langevin function and truncated exponential di…
Usually, the transverse momentum distribution is described by a sum of an exponential decay term plus a decreasing power like contribution representing the soft non-perturbative and hard perturbative QCD collisions, respectively. In this…
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
In this paper we review and compare the numerical evaluation of those probability distributions in random matrix theory that are analytically represented in terms of Painlev\'e transcendents or Fredholm determinants. Concrete examples for…
The relativistic quantum equation is proposed for the complex wave function, which has the meaning of a probability amplitude. The Lagrangian formulation of the proposed theory is developed. The problem of spreading of a wave packet in an…
We investigate a recursively generated sequence of random variables that begins with an Exponential random variable with parameter (i.e., inverse-mean) 1, and continues with additional Exponentials, each of whose random parameter possesses…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
A simple integral relation between a complex weight and the corresponding positive distribution is derived by introducing a second complex variable. Together with the positivity and normalizability conditions, this sum rule allows to…
In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where $X=\{X(t)\}$ is a spectrally positive L\'evy process and $c\in\RL$. As an example we investigate the inverse Gaussian L\'evy process.
The Lindley distribution was first introduced by Lindley in 1958 for Bayesian computations. Over the past years, various generalizations of this distribution have been proposed by different authors. The generalized Lindley distributions…
The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood…
The problem of finding a positive distribution, which corresponds to a given complex density, is studied. By the requirement that the moments of the positive distribution and of the complex density are equal, one can reduce the problem to…
Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
We propose estimators for the parameters of the Linnik L$(\alpha,\gamma)$ distribution. The estimators are derived from the moments of the log-transformed Linnik distributed random variable, and are shown to be asymptotically unbiased. The…