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Abstract:
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Estimation of heavy-tailed distributions has a long history and such distributions play a fundamental role in estimating the occurrence of extreme events (e.g., very high or cold temperatures, huge earthquakes, storm surge, sudden large fluctuations in stock market). Several parametric classes of models are used to capture the tails of various subclasses of distributions (e.g., fat-tailed, long-tailed and sub-exponential distributions). This paper develops a nonparametric class of distributions based on a mixture of scaled Beta distributions with tail adjustments that is flexible to capture different types of tail behaviors of the underlying distributions. A computationally efficient algorithm is presented that allows for the estimation of the density based on maximizing a sieve of likelihood functions as the number of mixture components grows with sample size. Numerical illustrations are presented with simulated and real data sets.
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