  Frequency power spectra due to a super-position of uncorrelated Lorentzian
pulses with a random distribution of amplitudes are considered. For pulses with
constant duration, there is an exponential frequency spectrum which is
independent of the degree of pulse overlap and the pulse amplitude
distribution. The spectrum is furthermore shown to be unaffected by skewness of
the Lorentzian pulses and even a random distribution of the pulse asymmetry
parameter and its correlation with the pulse amplitude. This stochastic model
provides new insight to the ubiquitous exponential spectra in fluids and
magnetized plasmas exhibiting deterministic chaos, where non-linear advection
processes lead to amplitude dependent steepening of smooth pulses.
