Abstract

Let ξ be a random variable (r.v.) with the characteristic function φ(t) and ν be a r.v. with generating function a(z),ν being independent of ξ. It is known that the composed r.v. η of ξ and ν (denoted by η=<ν,ξ>) is the r.v. having the characteristic function ψ(t)=a[φ(t)]. The r.v. ν is called the first component of η and ξ the second component of η. We investigate the changes of the distribution function of the composed r.v. η if we have the small changes of the distribution function of the first component ν or the second component ξ of η.