On the stability estimation of Wang's characterization theorem

Abstract

An important and useful characterization of the Weibull distribution is its lack of memory (of order a) property, i.e., P (X ≥ ^a√(x^a + y^a)|X ≥ y ) = P(X ≥ x) for all x, y ≥ 0. The technique commonly employed in proving this characterization is the well-known Cauchy functional equ­ation φ(^a√(x^a + y^a)) = φ(x)φ(y). The stability estimation in this characterization of the Weibull distribution is analysied.