Where does tail collide?

The region of a probability distribution far from its centre, where values become rare but not impossible: the tail describes how fast probability falls away toward the extremes, and a heavy or fat tail is one that decays slowly, so large deviations stay more likely than a normal curve would predict. Mandelbrot's 1963 The variation of certain speculative prices argued that price changes follow such heavy-tailed distributions rather than a Gaussian, so the tail carries the risk of the rare, large move. The referent is a part of a probability distribution, described by its rate of decay and its tail probability, not an appendage on an animal, the end of a list in a program, or the rear of an aircraft.[1]

Unit

The probability mass beyond an extreme threshold of a distribution

Recovery means

Not applicable

Measured by

Estimated from the far quantiles of a sample, by a fitted tail index or the exceedance probability above a high threshold

In computer science the tail is what remains of a list once its first element, the head, is removed, so a list is read as a head followed by its tail; the same word names a call made in tail position, the last action of a procedure, which a tail-recursive process can carry out without growing the stack. Abelson and Sussman's Structure and interpretation of computer programs set out how such tail calls let an iterative computation run in constant space. The referent is a construct of programs and data structures, defined by structure and control flow, not a part of an animal, a region of a distribution, or the rear of an aircraft.[2]

Unit

The list remaining after its head, or a procedure call in tail position

Recovery means

Not applicable

Measured by

Identified structurally: the tail is what is left of a list after its head, and a tail call is a call in the final position of a procedure