  A random phenomenon may have two sources of random variation: an unstable
identity and a set of external variation-generating factors. When only a single
source is active, two mutually exclusive extreme scenarios may ensue that
result in the exponential or the normal, the only truly univariate
distributions. All other supposedly univariate random variation observed in
nature is truly bivariate. In this article, we elaborate on this new paradigm
for random variation and develop a general bivariate distribution to reflect
it. It is shown that numerous current univariate distributions are special
cases of an approximation to the new bivariate distribution. We first show that
the exponential and the normal are special cases of a single distribution
represented by a Response Modeling Methodology model. We then develop a general
bivariate distribution commensurate with the new paradigm, its properties are
discussed and its moments developed. An approximating assumption results in a
univariate general distribution that is shown to include as exact special cases
widely used distributions like generalized gamma, log-normal, F, t, and Cauchy.
Compound distributions and their relationship to the new paradigm are
addressed. Empirical observations that comply with predictions derived from the
new paradigm corroborate its scientific validity.
