  We show analytically that the answer to the question, "The longer it has been
since the last earthquake, the longer the expected time till the next ?"
depends crucially on the statistics of the fluctuations in the interval times
between earthquakes. The periodic, uniform, semigaussian, Rayleigh and
truncated statistical distributions of interval times, as well as the Weibull
distributions with exponent greater than 1, all have decreasing expected time
to the next earthquake with increasing time since the last one, for long times
since the last earthquake; the log-normal and power-law distributions and the
Weibull distributions with exponents smaller than 1, have increasing times to
the next earthquake as the elapsed time since the last increases, for long
elapsed times. There is an identifiable crossover between these models, which
is gauged by the rate of fall-off of the long-term tail of the distribution in
comparison with an exponential fall-off. The response to the question for short
elapsed times is also evaluated. The lognormal and power-law distributions give
one response for short elapsed times and the opposite for long elapsed times.
Even the sampling of a finite number of intervals from the Poisson distribution
will lead to an increasing estimate of time to the next earthquake for
increasing elapsed time since the last one.
