The
stretched exponential function
is obtained by inserting a fractional
power law into the
exponential function. In most applications, it is meaningful only for arguments
t between 0 and +8. With
ß = 1, the usual exponential function is recovered. With a
stretching exponent ß between 0 and 1, the graph of log
f versus
t is characteristically
stretched, whence the name of the function. The
compressed exponential function (with
ß > 1) has less practical importance, with the notable exception of
ß = 2, which gives the
normal distribution.