  N.L. Johnson and S. Kotz introduced in 1990 an interesting family of
symmetric distributions which is based on randomly weighted average from
uniform random samples. The only example that could be addressed to their work
is the so-called "uniformly randomly modified tin" distribution from which two
random samples have been computed. In this paper, we generalize a subfamily of
their symmetric distributions and identify a concrete instance of this
generalized subfamily. That instance turns out to belong to the family of
Johnson and Kotz, which had not seemingly received proper attention in the
literature.
