Reliable use of -value in [()] = − is critical in seismicity comparisons, seismic hazard analysis, prediction and comparative mechanism studies. Since earthquakes and the -value are considered as stochastic processes and random variable, respectively, applying the probability distribution of -value is necessary in its temporal and spatial variations assessment. In this paper, we propose a novel method that employs the -value uncertainty in probabilistic seismic hazard analysis using normal-exponential joint distribution function. To this end, we calculate -value statistics based on bootstrap sampling of the seismic catalog. Our analytical and experimental evaluations show that the proposed joint distribution results in a more precise closed-form relation for the probabilistic seismic hazard analysis accurately reducing the hazard in comparison to conventional methods. The benefit of the proposed approach here is improving the ability of assessing the effectiveness of various seismic risk mitigation strategies and so, allocates the available resources more efficiently.
