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A Student Process with Application to SOI Data

M.T. Alodat, K.M. Aludaat


We generalize the Gaussian process to a non-Gaussian process. The new process has heavier tail distribution than the Gaussian one. We call the new process as the student process. We derive the expected number of up-crossings for this process. We derive a heuristic approximation to the duration distribution of its excursion above a high threshold. We also derive its up-crossing rate. We compare this approximation with the exact data via simulation. We apply our finding to the SOI (Southern Oscillation Index) data.


Gaussian process, up-crossing, Rice’s formula, excursion set, student process

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