A new extreme value copula and new families of univariate distributions based on Freund’s exponential model

The use of the exponential distribution and its multivariate generalizations is extremely popular in lifetime modeling. Freund's bivariate exponential model (1961) is based on the idea that the remaining lifetime of any entity in a bivariate system is shortened when the other entity defaults. Such a model can be quite useful for studying systemic risk, for instance in financial systems. Guzmics and Pflug (2019) revisited Freund's model, deriving the corresponding bivariate copula and examined some characteristics of it; furthermore, we opened the door for a multivariate setting. Now we present further investigations in the bivariate model: we compute the tail dependence coefficients, we examine the marginal and joint distributions of the componentwise maxima, which leads to an extreme value copula, which - to the best of our knowledge - has not been investigated in the literature yet. The original bivariate model of Freund has been extended to more variables by several authors. We also turn to the multivariate setting, and our focus is different from that of the previous generalizations, and therefore it is novel: examining the distribution of the sum and of the average of the lifetime variables (provided that the shock parameters are all the same) leads to new families of univariate distributions, which we call Exponential Gamma Mixture Type I and Type II (EGM) distributions. We present their basic properties, we provide asymptotics for them, and finally we also provide the limiting distribution for the EGM Type II distribution

Modelling cascading effects for systemic risk: Properties of the Freund copula

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

Reconstruction of magma chamber processes preserved in olivine-phlogopite micro-ijolites from the Oldoinyo Lengai, Tanzania

A detailed petrographic and mineralogical investigation of olivine-phlogopite micro-ijolite xenoliths from Oldoinyo Lengai, Tanzania indicates a complex evolutional history. These xenoliths consist of diverse textural subdomains characterized by minerals ranging from early-formed olivine, through diopside-hosted perovskite and phlogopite, to evolved aegirine-augite and titanite. Thermometry and mineral compositions in the subdomains suggest crystallization temperatures from 1070–970 °C to 850–700 °C at plutonic pressures and SiO2-activities controlled by perovskite-titanite equilibria. Double coronas are a characteristic textural feature of the olivine-phlogopite micro-ijolite, consisting of olivine cores surrounded by an inner clinopyroxene corona and an outer phlogopite corona. These double coronas might have formed during early magma chamber processes, including magma movement to a subsequent chamber resulting in dissolution of olivine with subsequent crystallization and accumulation of diopside and phlogopite. Diopside−aegirine-augite compositional zonation indicates several magma injections followed by cooling periods, during the formation of micro-ijolite groundmass. Mg# (80–83) and Ca (0.1–0.3 in wt%) contents of olivine together with the presence of primary melt inclusions in clinopyroxene, phlogopite, and nepheline indicate a magmatic origin from a possible parental olivine-nephelinite melt. There is evidence for subsolidus, or near-solidus, re-equilibration processes as indicated by the reaction of olivine with titanite forming symplectitic textures of ilmenite and diopside with minor zirconolite. Ti-exchange between phlogopite phenocrysts and other Ti-bearing minerals (perovskite, titanite, magnetite) resulted in ∼750 °C equilibrium temperatures for phlogopite, which are much lower than mafic magmatic (>900 °C) conditions. Calculated subsolidus temperatures suggest crystallization of olivine-phlogopite micro-ijolites over a 10–20 km depth interval

A háztáji gazdaság, mint a termelőszövetkezet gazdálkodásának szerves része

INST: L_08

A szemléletformálás, mint a vállalati felelősségvállalás egyik hatékony eszköze

A természeti és az emberi környezet védelme minden egyes embert érintő tevékenység. A környezeti szennyezés mára olyan mértékűvé vált, hogy (intézményi szinten) nem elég megfelelni a vonatkozó jogszabályoknak, újabb módokat kell találnunk, amellyel nemcsak felhívni tudjuk az emberek figyelmét, hanem cselekvésre, megelőzésre is ösztönözhetjük őket. A környezeti tudatosság megteremtése nagyon komplex, összetett, új világszemlélet. Az összetettségben, az egységben való szemléletről szól, mint ahogy maga az ökológia is működik. Környezettudatosan gondolkodó és cselekvő polgárokra van szükség – az átgondolt beruházások és a hosszú, tudatos, következetes fejlesztés mellett. Mindehhez az integrált vállalati felelősségvállalás megfelelő keretet nyújt.régi képzésKörnyezetvédelmi és -fejlesztési szaktanácsadó szakg