Expectation identities based on recurrence relations of functions of generalized order statistics

Some recurrence relations between expectation of function on single and joint
generalized order statistics for a general class of distribution

    \begin{align*} 1 − F(x) = \exp \Big[ -\frac{1}{c} \{ h(x)-h(\alpha)\} \Big], \alpha<x<\beta \end{align*}

are obtained. Further, various deductions and particular cases are also discussed.
Keywords and phrases: Order statistics, record values, sequential order statistics,
Burr, power function; Pareto and Weibull distributions.