  We derive strong laws of large numbers and central limit theorems for
Bajraktarevi\'c, Gini and exponential- (also called Beta-type) and logarithmic
Cauchy quotient means of independent identically distributed (i.i.d.) random
variables. The exponential- and logarithmic Cauchy quotient means of a sequence
of i.i.d. random variables behave asymptotically normal with the usual square
root scaling just like the geometric means of the given random variables.
Somewhat surprisingly, the multiplicative Cauchy quotient means of i.i.d.
random variables behave asymptotically in a rather different way: in order to
get a non-trivial normal limit distribution a time dependent centering is
needed.
