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distributions) from NEF-QVF and NEF-CVF. The aim is twofold, first we want to illustrate by the examples that the bounds maywell be used as approximation of unknown variances and secondly we want to compare the two bounds to show that sometimes the calculation of the Bhattacharyya bound is sufficient since the Kshirsagar bound is only marginally larger but much more difficult to compute. Keywords: Cramér–Rao bound, Quadratic Exponential Family (NEF-QVF), Cubic Exponential Family (NEF- CVF), Hammersley–Chapman–Robbins bound. MSC 2010: 62E10, 62F99, 65D99 DOI 10.1515/eqc-2014

representations, and limiting distributions of random sums with discrete-Pareto number of terms. We also briey discuss issues of simulation and estimation and extensions to multivariate setting. Keywords:GeometricDistribution,HeavyTails, InniteDivisibility, LomaxDistribution,MultivariateDiscrete Distribution, Pareto Distribution, Power Law, Random Sum, Yule Distribution MSC 2010: 60E05, 60E07, 62E10, 62E15 DOI: 10.1515/eqc-2014-0014 Received October 21, 2014; revised November 12, 2014; accepted November 26, 2014 1 Introduction The objective of this paper is a study of a family

Abstract

A new measure of dependence called pseudo-covariance and related to covariance is proposed. It can be applied in problems when the classic covariance fails. We show that it can be used as a measure of dependence of uncorrelated random variables and in characterizations of continuous distributions (here power distribution on (0, 1) and exponential distribution).

Abstract

We review various methods for constructing bivariate copulas with given diagonal sections from seminal work to the most recent research on copulas with given diagonal and opposite diagonal sections. A survey on a generalization of copulas with given diagonal plane sections in higher dimensions and other sections that generalize the diagonal and opposite diagonal sections is of particular interest.

Abstract

We consider a dependent lifetime model for systemic risk, whose basic idea was for the first time presented by Freund. This model allows to model cascading effects of defaults for arbitrarily many economic agents. We study in particular the pertaining bivariate copula function. This copula does not have a closed form and does not belong to the class of Archimedean copulas, either.We derive some monotonicity properties of it and show how to use this copula for modelling the cascade effect implicitly contained in observed CDS spreads.

Abstract

Fiscal policy includes the government decisions on the size of taxes that affect the size of the government deficit. There are different types of government deficit. The aim of the analyses is to examine the relation between the type of deficit and the optimal level of tax rate. In this article we verify the hypothesis that the type of deficit considered affects the tax rate. For the hypothesis verification, we use the feedback rules that are the solution of the quadratic-linear problem.

Abstract

If the distribution of the linear combination of two independent and identically distributed random variables from a distribution belongs to the same distribution, then we call that distribution a stable distribution. The Levy distribution is a member of the family of stable distributions. In this paper, we will present some basic distributional properties and characterizations of the Levy distribution.

Abstract

Motivated by the nice characterization of copulas A for which d(A, At) is maximal as established independently by Nelsen [11] and Klement & Mesiar [7], we study maximum asymmetry with respect to the conditioning-based metric D1 going back to Trutschnig [12]. Despite the fact that D1(A, At) is generally not straightforward to calculate, it is possible to provide both, a characterization and a handy representation of all copulas A maximizing D1(A, At). This representation is then used to prove the existence of copulas with full support maximizing D1(A, At). A comparison of D1- and d-asymmetry including some surprising examples rounds off the paper.

Abstract

Heyde proved that a Gaussian distribution on a real line is characterized by the symmetry of the conditional distribution of one linear form given another. The present article is devoted to an analogue of the Heyde theorem in the case when random variables take values in a locally compact Abelian group and the coefficients of the linear forms are integers.

Abstract

In this article, we introduce some examples of cubic rank transmuted distributions proposed by Granzatto et al. (2017). The statistical aspects of the introduced distributions such as probability density functions, hazard rate functions and reliability functions are studied. The maximum likelihood estimation method is used in order to estimate the parameters of interest. Finally, real data examples are applied for the illustration of these distributions.