6 research outputs found
General inverse problems for regular variation
Regular variation of distributional tails is known to be preserved by various
linear transformations of some random structures. An inverse problem for
regular variation aims at understanding whether the regular variation of a
transformed random object is caused by regular variation of components of the
original random structure. In this paper we build up on previous work and
derive results in the multivariate case and in situations where regular
variation is not restricted to one particular direction or quadrant
Extremes of Aggregated Dirichlet Risks
The class of Dirichlet random vectors is central in numerous probabilistic
and statistical applications. The main result of this paper derives the exact
tail asymptotics of the aggregated risk of powers of Dirichlet random vectors
when the radial component has df in the Gumbel or the Weibull max-domain of
attraction. We present further results for the joint asymptotic independence
and the max-sum equivalence.Comment: published versio
Asymptotic tail behavior of phase-type scale mixture distributions
We consider phase-type scale mixture distributions which correspond to
distributions of a product of two independent random variables: a phase-type
random variable and a nonnegative but otherwise arbitrary random variable
called the scaling random variable. We investigate conditions for such a
class of distributions to be either light- or heavy-tailed, we explore
subexponentiality and determine their maximum domains of attraction. Particular
focus is given to phase-type scale mixture distributions where the scaling
random variable has discrete support --- such a class of distributions has
been recently used in risk applications to approximate heavy-tailed
distributions. Our results are complemented with several examples.Comment: 18 pages, 0 figur