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CMPH: a multivariate phase-type aggregate loss distribution

Jiandong Ren;  Ricardas Zitikis — 2017

Dependence Modeling

We introduce a compound multivariate distribution designed for modeling insurance losses arising from different risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses.We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations...

Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment

Danang Teguh Qoyyimi;  Ricardas Zitikis — 2015

Dependence Modeling

Measuring association, or the lack of it, between variables plays an important role in a variety of research areas, including education,which is of our primary interest in this paper. Given, for example, student marks on several study subjects, we may for a number of reasons be interested in measuring the lack of comonotonicity (LOC) between the marks, which rarely follow monotone, let alone linear, patterns. For this purpose, in this paperwe explore a novel approach based on a LOCindex,which is...

Grüss-type bounds for covariances and the notion of quadrant dependence in expectation

Martín Egozcue;  Luis García;  Wing-Keung Wong;  Ričardas Zitikis — 2011

Open Mathematics

We show that Grüss-type probabilistic inequalities for covariances can be considerably sharpened when the underlying random variables are quadrant dependent in expectation (QDE). The herein established covariance bounds not only sharpen the classical Grüss inequality but also improve upon recently derived Grüss-type bounds under the assumption of quadrant dependency (QD), which is stronger than QDE. We illustrate our general results with examples based on specially devised bivariate distributions...

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