The Lindy effect is a statistical tendency for things with longer pasts behind them to have longer futures ahead.

While the Lindy effect is often thought to require a declining hazard rate, I show that it arises very naturally even in cases with constant (or increasing) hazard rates — so long as there is a probability distribution over the size of that rate.

even things which are becoming less robust over time can display the Lindy effect.

The Lindy effect is a statistical regularity where for many kinds of entity: the longer they have been around so far, the longer they are likely to last. This was first clearly posed by Benoît Mandelbrot (1982, p. 342) in his book, The Fractal Geometry of Nature

The idea was developed by Nassim Taleb (2012) in his book, Antifragile. The book focused on a special category of entities: those which aren’t weakened by exposure to shocks and stresses, but which instead become stronger and more robust.

in studying the Lindy effect it is most convenient to adopt the methods of survival analysis (Miller 2011) and think in terms of the distribution’s survival function, S(t), and hazard function, λ(t).

if the hazard rate were to decline monotonically over time, then the survival curve would decline more slowly than an exponential (such distributions are known as heavy-tailed). This implies that the time needed for survival to halve would keep getting longer the more time that has elapsed

here is a close connection between the Lindy effect and power law distributions (a subset of heavy-tailed distributions).

in the latter years of our lives, the hazard rate rises exponentially. It thus may not be that humans are crisply in a category of ‘perishable’ things with hard upper bounds on our lifespans, but rather than we are in the more subtle category of things with exponentially increasing hazard.