Longman Dictionary of Contemporary English
Douglas Harper's Etymology Dictionary
1778, an arbitrary formation, part of what Farmer describes as "A class of colloquialisms compounded with an intensive prefix" (ram- or rum-), probably suggesting in part rum (adj.) in its old slang sense of "good, fine," and ramp (n.2). In this case apparently suggested by boisterous, robustious, bumptious, etc. Coined about the same time were rumbustical, rambumptious "conceited, self-assertive," ramgumptious "shrewd, bold, rash," rambuskious "rough," rumstrugenous. Also compare ramshackle, rambunctious.\n\n
Wiktionary
a. (context informal chiefly British English) boisterous and unruly
WordNet
adj. noisy and lacking in restraint or discipline; "a boisterous crowd"; "a social gathering that became rambunctious and out of hand"; "a robustious group of teenagers"; "beneath the rumbustious surface of his paintings is sympathy for the vulnerability of ordinary human beings"; "an unruly class" [syn: boisterous, rambunctious, robustious, unruly]
Usage examples of "rumbustious".
It had been bought and brought to greatness in the fifties by a rumbustious tycoon thrown up atypically from prudent banking stock.
The second small blot in the clear sky was an urchin with a broken head, who admitted, between sniffs and sobs, that he and a few more of his age had been playing a somewhat rumbustious ball game against the wall of the priests house, a clear, windowless wall well suited for the purpose, and that they had naturally made a certain amount of noise in the process.