相关论文: Positive-part moments via the characteristic funct…
Integral expressions for positive-part moments E X_+^p (p>0) of random variables X are presented, in terms of the Fourier-Laplace or Fourier transforms of the distribution of X. A necessary and sufficient condition for the validity of such…
The absolute moments of probability distributions are much more complicated than conventional ones. By using a direct and simpler approach, we retreat P. L. Hsu's (1951, J. Chinese Math. Soc., Vol. 1, pp. 257-280) formulas in terms of the…
Let $X$ be an arbitrary real-valued random variable (r.v.), with the characteristic function (c.f.) $f$. Integral expressions for the c.f.\ of the r.v.'s $\max(0,X)$ in terms of $f$ are given, as well as other related results. Applications…
Expressions are given for the truncated fractional moments $E X_+^p$ of a general stable law. These involve families of special functions that arose out of the study of multivariate stable densities and probabilities. As a particular case,…
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the…
Let a ``complex probability'' be a normalizable complex distribution $P(x)$ defined on $\R^D$. A real and positive probability distribution $p(z)$, defined on the complex plane $\C^D$, is said to be a positive representation of $P(x)$ if…
Inspired by Stein's lemma, we derive two expressions for the joint moments of elliptical distributions. We use two different methods to derive $E[X_{1}^{2}f(\mathbf{X})]$ for any measurable function $f$ satisfying some regularity…
We introduce a novel method for obtaining a wide variety of moments of any random variable with a well-defined moment-generating function (MGF). We derive new expressions for fractional moments and fractional absolute moments, both central…
The main purpose of this work is to prove characterization theorems for generalized moment functions on groups. According one of the main results these are exponential polynomials that can be described with the aid of complete (exponential)…
Factorial moments and cumulants are usually defined with respect to the unconditioned Poisson process. Conditioning a sample by selecting events of a given overall multiplicity $N$ necessarily introduces correlations. By means of Edgeworth…
This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored, and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact…
Fractional moments have been investigated by many authors to represent the density of univariate and bivariate random variables in different contexts. Fractional moments are indeed important when the density of the random variable has…
The main goal of this research is to model and investigate generalizations of functions from [31]. Arguments of modeled functions are presented by the representation $\pi_{\mathfrak p}$ from [22].
We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
The family of multivariate skew-normal distributions has many interesting properties. It is shown here that these hold for a general class of skew-elliptical distributions. For this class, several stochastic representations are established…
We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous transition functions and are in duality with standard processes…
The method of \emph{random integral representation}, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note we will…
For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…