  The joint eigenvalue distributions of random-matrix ensembles are derived by
applying the principle maximum entropy to the Renyi, Abe and Kaniadakis
entropies. While the Renyi entropy produces essentially the same matrix-element
distributions as the previously obtained expression by using the Tsallis
entropy, and the Abe entropy does not lead to a closed form expression, the
Kaniadakis entropy leads to a new generalized form of the Wigner surmise that
describes a transition of the spacing distribution from chaos to order. This
expression is compared with the corresponding expression obtained by assuming
Tsallis' entropy as well as the results of a previous numerical experiment.
