On distributions having the almost-lack-of-memory property
Stefanka S. Chukova, Boyan N. Dimitrov · Journal of Applied Probability · 1992
It is shown that random variables X exist, not exponentially or geometrically distributed, such that P{X – b ≧ x | X ≧ b} = P{X ≧ x} for all x > 0 and infinitely many different values of b. A class of distributions having the given property is exhibited. We call them ALM distributions, since they almost have the lack-of-memory property. For a given subclass of these distributions some phenomena relating to service by an unreliable server are discussed.