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producer’s and consumer’s risks for specified Acceptable Quality Level and Limiting Quality Level using weighted Poisson distribution. Keywords: Acceptable Quality Level (AQL), Attribute Plan, Limiting Quality Level (LQL), MinimumRisk Plan. MSC 2010: 90B40, 60E05 || *Corresponding Author: Kandasamy Subramani, Department of Statistics, Government Arts College, Coimbatore – 641018, India, e-mail: subbugow@yahoo.com Venugopal Haridoss: Science and Humanities Department (Mathematics division), Kumaraguru College of Technology, Coim- batore – 641049, India, e-mail: venuhari77

various methods of estimation is also considered and demonstrated with the help of a real data set. Keywords:Confluent hypergeometric series, Displaced Poisson, distribution, Factorialmoments, Poissondis- tribution of order 𝑘, Probability generating function. MSC 2010: 60E05, 60E10, 33C20 || *Corresponding Author: C. Satheesh Kumar, University of Kerala, Trivandrum -695 581, India, e-mail: drcsatheeshkumar@gmail.com B. Unnikrishnan Nair: University of Kerala, Trivandrum -695 581, India 1 Introduction Bardwell and Crow [3] have considered a two-parameter generalization

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We present an analytical proof of the characterisation of bivariate Archimax copulas in terms of the properties of their generating functions.

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We discuss a new construction method for obtaining additive generators of Archimedean copulas proposed by McNeil, A. J.-Nešlehová, J.: Multivariate Archimedean copulas, d-monotone functions and l1-norm symmetric distributions, Ann. Statist. 37 (2009), 3059-3097, the so-called Williamson n-transform, and illustrate it by several examples. We show that due to the equivalence of convergences of positive distance functions, additive generators and copulas, we may approximate any n-dimensional Archimedean copula by an Archimedean copula generated by a transformation of weighted sum of Dirac functions concentrated in certain suitable points. Specifically, in two dimensional case this means that any Archimedean copula can be approximated by a piece-wise linear Archimedean copula, moreover the approximation of generator by linear splines circumvents the problem with the non-existence of explicit inverse.

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

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We provide an explicit expression for the quantile of a mixture of two random variables. The result is useful for finding bounds on the Value-at-Risk of risky portfolios when only partial dependence information is available. This paper complements the work of [4].

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We provide combinatorial as well as probabilistic interpretations for the q-analogue of the Pochhammer k-symbol introduced by Díaz and Teruel. We introduce q-analogues of the Mellin transform in order to study the q-analogue of the k-gamma distribution.

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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.

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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.

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The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.