Abstract
The generalized Pareto distribution is one of the popular models in the environmental sciences. Scientists in these areas are often interested in comparing the values of an environmental variable under two different conditions, locations, etc. This would require the study of the ratio X/(X+Y) where X and Y are independent generalized Pareto random variables. In this note, the exact distribution of X/(X+Y) is derived, which turns out to involve the Gauss hypergeometric function. An application of this result is provided to assess the relative extremity of rainfall for 14 locations in Florida. Some computer programs for use in the applications are also provided.
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The authors would like to thank the Editor-in-Chief and the referees for carefully reading the paper and for their great help in improving the paper.
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Nadarajah, S., Kibria, B.M.G. Ratio of generalized random variables with application. Stoch Environ Res Ris Assess 20, 206–212 (2006). https://doi.org/10.1007/s00477-005-0003-8
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DOI: https://doi.org/10.1007/s00477-005-0003-8