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One of the most difficult tasks in the solution of a hypothesis testing problem is the estimation of the probability density functions of the null and the alternative hypothesis. In this paper, the simultaneous detection of seismic events contained in a given data record is formulated as such a problem and an approximation of the probability density function under the null hypothesis, of a ratio based test statistic is proposed. By exploiting some interesting properties satisfied by the ratio of identical distributed Random Variables, as well as the sparsity of the seismic events in the data record, we succeed in obtaining such an approximation. From a series of experiments we have conducted in both synthetic and real seismic data, the effectiveness of the proposed technique is confirmed.