  This paper derives the distribution of the maximum end-to-end (e2e) signal to
noise ratio (SNR) in an opportunistic relay selection based cooperative
relaying (CR) network having large number of non-identical relay links between
the source and destination node. The source node is assumed to be simultaneous
wireless information and power transfer (SWIPT) enabled and the relays are
capable of both time splitting (TS) and power splitting (PS) based energy
harvesting (EH). Contrary to the majority of literature in communication, which
uses extreme value theory (EVT) to derive the statistics of extremes of
sequences of independent and identically distributed (i.i.d.) random variables
(RVs), we demonstrate how tools from EVT can be used to derive the asymptotic
statistics of sequences of independent and non-identically distributed
(i.n.i.d.) normalised SNR RVs and hence characterise the distribution of the
maximum e2e SNR RV. Using these results we derive the expressions for ergodic
and outage capacities at the destination node. Finally, we present the utility
of the asymptotic results for deciding the optimum TS and PS factors of the
hybrid EH relays that (i) minimise outage probability and (ii) maximise ergodic
capacity at the destination. Furthermore, we demonstrate how stochastic
ordering results can be utilised for simplifying these optimisation problems.
