Related papers: On sampling and parametrization of discrete freque…
A most debated topic of the last years is whether simple statistical physics models can explain collective features of social dynamics. A necessary step in this line of endeavour is to find regularities in data referring to large scale…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
This paper investigates the effects of data size and frequency range on distributional semantic models. We compare the performance of a number of representative models for several test settings over data of varying sizes, and over test…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
In population genetics, diffusions on the unit interval are often used to model the frequency path of an allele. In this setting we derive approximations for fixation probabilities, expected hitting times and the expected…
Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
The problem of the estimation of relevance to a set of histograms generated by samples of a discrete time process is discussed on the base of the variational principles proposed in the previous paper [1]. Some conditions for dimension…
The distribution of the sum of independent identically distributed uniform random variables is well-known. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the…
A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite…
We investigate the performance and sampling variability of estimated forecast combinations, with particular attention given to the combination of forecast distributions. Unknown parameters in the forecast combination are optimized according…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…
In the paper, multivariate probability distributions are considered that are representable as scale mixtures of multivariate elliptically contoured stable distributions. It is demonstrated that these distributions form a special subclass of…
We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…