Runuran is a wrapper to UNU.RAN (Universal Non-Uniform RANdom variate generators), a library for generating random variates for large classes of distributions. It also allows to compute quantiles (inverse cumulative distribution functions) of these distributions efficiently. In addition it can be used to compute (approximate) values of the density function or the distribution function. In order...

In this paper, we study properties of exp-uniform distribution and its applications. We provide closed forms for the density function and moments of order statistics and we also discuss estimation of the parameters via the maximum likelihood method. We will present certain characterizations of exp-uniform distribution. The applications of this distribution are illustrated by fitting it to three...

Transfer-matrix methods are used to calculate spin-spin correlation functions (G), Helmholtz free energies (f) and magnetizations (m) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature T(c 0), on long strips of width L=3-18 sites, for binary field distributions. Analysis of the probability distributions of G for varying spin-spin distances R shows ...

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total variation point of view. To do this, we construct statistics that measure, in a certain well-defined sense, global “balancedness” properties of such trees. Our...

Continuous probability distributions are widely used to mathematically describe random phenomena in engineering and physical sciences. In this paper, we present a methodology that can be used to formalize any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Our methodology is primarily based on the Standard ...

It is required to suppress or mitigate the optical signal distortion due to group velocity dispersion and optical Kerr effects in ultra-high speed and long-haul transmission systems. Dispersion management (DM), optical phase conjugation (OPC), and the combination of these two are promising techniques to compensate for the signal distortion. The goal of this paper is to investigate the possibili...