Related papers: Distribution and asymptotics under beta random sca…
We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…
We provide a necessary and sufficient condition for the ratio of two jointly alpha-Frechet random variables to be regularly varying. This condition is based on the spectral representation of the joint distribution and is easy to check in…
Association models for a pair of random elements $X$ and $Y$ (e.g., vectors) are considered which specify the odds ratio function up to an unknown parameter $\bolds\theta$. These models are shown to be semiparametric in the sense that they…
We discuss in this paper a possibility of constructing a whole class of asymptotic distribution-free tests for testing regularly varying tail distributions. The idea is that we treat the tails of distributions as members of a parametric…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
A compilation of new results on the asymptotic behaviour of the Humbert functions $\Psi_1$ and $\Psi_2$, and also on the Appell function $F_2$, is presented. As a by-product, we confirm a conjectured limit which appeared recently in the…
Multiplicative self-decomposable laws describe random variables that can be decomposed into a product of a scaled-down version of themselves and an independent residual term. Shanbhag et al.~(1977) have shown that the gamma distribution is…
If the step distribution in a renewal process has finite mean and regularly varying tail with index -{\alpha}, 1<{\alpha}<2, the first two terms in the asymptotic expansion of the renewal function have been known for many years. Here we…
In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes.…
We re-investigate the asymptotic properties of the traditional OLS (pooled) estimator, $\hat{\beta} _P$, in the context of cluster dependence. The present study considers various scenarios under various restrictions on the cluster sizes and…
In this paper, we study the asymptotic behavior of supremum distribution of some classes of iterated stochastic processes $\{X(Y(t)) : t \in [0, \infty)\}$, where $\{X(t) : t \in \mathbb{R} \}$ is a centered Gaussian process and $\{Y(t): t…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
Exploratory data analysis is often used to test the goodness-of-fit of sample observations to specific target distributions. A few such graphical tools have been extensively used to detect subexponential or heavy-tailed behavior in observed…
In this investigation, the distribution of the ratio of two independently distributed xgamma (Sen et al. 2016) random variables X and Y , with different parameters, is proposed and studied. The related distributional properties such as,…
We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…
The association between two random variables is often of primary interest in statistical research. In this paper semiparametric models for the association between random vectors X and Y are considered which leave the marginal distributions…
We study the asymptotic distribution, as the volume parameter goes to 1, of the peak (largest part) of finite- or slowly-growing-width cylindric plane partitions weighted by their trace, seam, and volume. There are two natural asymptotic…
Some asymptotic notions for random variables are discussed. In particular, different versions of O and o for sequences of random variables are studied. The results are elementary and more or less well-known, but collected here for future…
Let (X_n,Y_n), n\ge 1 be bivariate random claim sizes with common distribution function F and let N(t), t \ge 0 be a stochastic process which counts the number of claims that occur in the time interval [0,t], t\ge 0. In this paper we derive…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…