Related papers: The inverse of the cumulative standard normal prob…
We completely describe the asymptotic behaviour of the Riemann mapping function and its derivatives at an analytic cusp. We achieve the same for the inverse of the mapping function.
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
We derive in this article the asymptotic behavior as well as non-asymptotical estimates of tail of distribution for self-normalized sums of random variables (r.v.) under natural classical norming. We investigate also the case of…
We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
In two recent articles we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry {\it win-loss}. We present in…
We study odd numbers through a straightforward indexing. We focus in particular on odd prime and composite numbers and their distribution. With a counting argument, we calculate the limit of two sums and compare their convergence rate.
Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further…
Normal variance-mean mixtures encompass a large family of useful distributions such as the generalized hyperbolic distribution, which itself includes the Student t, Laplace, hyperbolic, normal inverse Gaussian, and variance gamma…
For general thinning procedures, its inverse operation, the condensing, is studied and a link to integration-by-parts formulas is established. This extends the recent results on that link for independent thinnings of point processes to…
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…
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…
A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…
Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is…
We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities of a general version of the game are investigated via…
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…
In one dimension, the theory of the $G$-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been…
We review basic ideas and basic examples of the theory of the inverse spectral problems.
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).