Probability gains expected for renewal process models

概要

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We usually use the Brownian distribution, lognormal distribution, Gamma distribution, Weibull distribution, and exponential distribution to calculate long-term probability for the distribution of time intervals between successive events. The values of two parameters of these distributions are determined by the maximum likelihood method. The difference in log likelihood between the proposed model and the stationary Poisson process model, which scores both the period of no events and instances of each event, is considered as the index for evaluating the effectiveness of the earthquake probability model. First, we show that the expected value of the log-likelihood difference becomes the expected value of the logarithm of the probability gain. Next, by converting the time unit into the expected value of the interval, the hazard is made to represent a probability gain. This conversion reduces the degrees of freedom of model parameters to 1. We then demonstrate that the expected value of the probability gain in observed parameter values ranges between 2 and 5. Therefore, we can conclude that the long-term probability calculated before an earthquake may become several times larger than that of the Poisson process model.
公益社団法人日本地震学会、地球電磁気・地球惑星圏学会、特定非営利活動法人日本火山学会、日本測地学会、日本惑星科学会の論文