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.