Related papers: On a six-parameter generalized Burr XII distributi…
A generalization of the generalized inverse Weibull distribution so-called transmuted generalized inverse Weibull dis- tribution is proposed and studied. We will use the quadratic rank transmutation map (QRTM) in order to generate a…
A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th…
In this paper we propose a new family of distribution considering Generalized Marshal-Olkin distribution as the base line distribution in the Beta-G family of Construction. The new family includes Beta-G (Eugene et al. 2002 and Jones, 2004)…
This paper extends earlier work on the distribution in the complex plane of the roots of random polynomials. In this paper, the random polynomials are generalized to random finite sums of given "basis" functions. The basis functions are…
In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…
In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size.…
The probability density function of Kerr effect phase noise, often called the Gordon-Mollenauer effect, is derived analytically. The Kerr effect phase noise can be accurately modeled as the summation of a Gaussian random variable and a…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
We obtain exact formulas for the cumulative distribution function of the variance-gamma distribution, as infinite series involving the modified Bessel function of the second kind and the modified Lommel function of the first kind. From…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…
We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the…
This study focuses on statistical inference for compound models of the form $X=\xi_1+\ldots+\xi_N$, where $N$ is a random variable denoting the count of summands, which are independent and identically distributed (i.i.d.) random variables…
Ensembles of random density matrices determined by various probability measures are analysed. A simple and efficient algorithm to generate at random density matrices distributed according to the Bures measure is proposed. This procedure may…
We propose a two-parameter bounded probability distribution called the extended power distribution. This distribution on $(0, 1)$ is similar to the beta distribution, however there are some advantages which we explore. We define the moments…
Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic…
This paper examines the classical matching distribution arising in the "problem of coincidences". We generalise the classical matching distribution with a preliminary round of allocation where items are correctly matched with some fixed…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
This work studies the chord length distribution, in the case where both ends lie on a $N$-dimensional hypersphere ($N \geq 2$). Actually, after connecting this distribution to the recently estimated surface of a hyperspherical cap…