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