Related papers: Notes on the sum and maximum of independent expone…
Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $ X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are…
We construct a non - improved exponential bounds for distribution of normed sums of i.,i.d. random variables with random numbers of summand.
The statistical properties of the multivariate Gamma-Gamma ($\Gamma \Gamma$) distribution with arbitrary correlation have remained unknown. In this paper, we provide analytical expressions for the joint probability density function (PDF),…
The statistical properties of the $E \times B$ flux in different types of plasma turbulence simulations are investigated using probability density distribution functions (PDF). The physics included in the models ranges from two dimensional…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
Let (W_i, J_i) be a sequence of i.i.d. R_+ x R-valued random vectors. Considering the partial sum of the first component and the corresponding maximum of the second component, we are interested in the limit distributions that can be…
We discuss the statistical properties of parton distributions within the framework of the NNPDF methodology. We present various tests of statistical consistency, in particular that the distribution of results does not depend on the…
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into…
The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(\alpha, \beta, \lambda)$ by giving explicit closed form expressions for its…
The sum of random variables (RVs) appears extensively in wireless communications, at large, both conventional and advanced, and has been subject of longstanding research. The statistical characterization of the referred sum is crucial to…
The evolution of probability distribution functions (PDFs) of continuous density, velocity and velocity derivatives ( deformation tensor) fields in the theory of cosmological gravitational instability are considered. We show that in the…
Conditional density estimation (CDE) is the task of estimating the probability of an event conditioned on some inputs. A neural network (NN) can also be used to compute the output distribution for continuous-domain, which can be viewed as…
The work of this paper is devoted to obtaining strong laws for intermediately trimmed sums of random variables with infinite means. Particularly, we provide conditions under which the intermediately trimmed sums of independent but not…
For a widely used hub-and-spoke closed product-form network consisting of an infinite-server node and several single-server queues, we characterize the maximum queue-length distribution in various operational regimes by leveraging a novel…
We consider the statistical properties of the gravitational field F in an infinite one-dimensional homogeneous Poisson distribution of particles, using an exponential cut-off of the pair interaction to control and study the divergences…
This paper presents the probability distribution function (p.d.f.) and cumulative distribution function (c.d.f.) of the weighted sum of central independent chi-squared random variables with non-zero weighs based on a method using moment…
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…
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables (not necessarily identically distributed), and $\eta$ be a counting random variable independent of this sequence. We obtain sufficient conditions on…
It is well-known that the expected scaled maximum of non-negative random variables with unit mean defines a stable tail dependence function associated with some extreme-value copula. In the special case when these random variables are…
A probability density function (pdf) encodes the entire stochastic knowledge about data distribution, where data may represent stochastic observations in robotics, transition state pairs in reinforcement learning or any other empirically…