Decomposition of weakly aging distributions

A class of weakly aging distribution functions is introduced and a number of properties of this class are derived. It is proved in particular that a random variable , having a weakly aging distribution function, can be written as a sum of two independent random variables, one of which has exponential distribution with a parameter equal to the modulus of the singular point of Me^–s nearest the coordinate origin.Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 571–574, October, 1977.