 All long-tailed distributions are heavy-tailed, but the converse is false, and it is possible to construct heavy-tailed distributions that are not long-tailed.Subexponentiality is defined in terms of convolutions of probability distributions.For two independent, identically distributed random variables formula_7 with common distribution function formula_8 the convolution of formula_8 with itself, formula_10 is convolution square, using Lebesgue–Stieltjes integration, by