A random power record model (Q1613009)

The authors study small-sample and asymptotic properties of record times and record counts in the random power record model introduced by them. For that random \(F^\alpha\) model, the joint c.d.f. of observations \(X_1, \dots,X_n\) is given by \[ G_n(x_1, \dots,x_n)= E\bigl\lfloor F^{\alpha_1} (x_1) \cdot\dots \cdot F^{\alpha_n} (x_n)\bigr \rfloor, \] where \(F\) is a continuous c.d.f., \(\alpha_1, \alpha_2,\dots\) are a.s. finite positive random variables and the expectation is taken with respect to the \(\alpha\)'s. The random \(F^\alpha\) model incorporates several record models proposed in the literature: the classical (i.i.d.), the Yang, the fixed \(F^\alpha\), the Ballerini and the NNB (Nezorova, Nevzorov and Balakrishnan) copula models.