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On Scale and Exponent Functions of a Class of Limiting Processes
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Suppose {Xn, n ∈ Z+) - see below for the notations used - is a sequence of random variables (rv's) such that, for every t > 0 and for ψ given by (1.1) below,
ψ(X(nt);αn;βn)->Y(t),
where Y\l) (in particular) is (assumed) nondegenerate. Then it is shown that, for some positive functions α and β on (0,∞) and for every t > 0,
Y(t)=ψ(Y(1);α(t),β(t))
Explicit expressions for a and p are derived. As an application, the (Pancheva) class of all possible limit laws for power normalized partial maxima of i.i.d rv's ("the p-max stable laws") is re-derived.
Keywords
Scale and Exponential Functions, P-Max Stable Laws, Limiting Processes.
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