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We investigate a way of comparing and classifying tails of random variables.Our approach extends the notion of classical indices, such as exponential andmoment indices, which are widely used measuring heaviness of tail functions. Anon-parametric risk measure applicable for all heavy-tailed random variables isobtained as a concave function that represents the decay speed of tailfunction. Many key properties of the distribution of a random variable areencoded into this function, which enables a new way to estimate tails. Thelatter half of the paper is devoted to numerous examples illustratingproperties of the results developed during the first half.

A comparison method for heavy-tailed random variables