156,877 research outputs found
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
Topologies of nodal sets of random band limited functions
It is shown that the topologies and nestings of the zero and nodal sets of
random (Gaussian) band limited functions have universal laws of distribution.
Qualitative features of the supports of these distributions are determined. In
particular the results apply to random monochromatic waves and to random real
algebraic hyper-surfaces in projective space.Comment: An announcement of recent results. Includes an announcement of the
resolution of some open questions from the older version. 11 pages, 6 figure
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