Denote f(x;μ,σ) and F(x;μ,σ), respectively, the p.d.f. and the c.d.f. of N(μ,σ^2). The p.d.f. and the c.d.f. of contaminated normal cN(μ,σ2,σc^2,p) (a N(μ,σ^2) contaminated in spread by a N(μ,σc^2) with probability p) are

(1-p)f(x;μ,σ)+pf(x;μ,σc) and

(1-p)F(x;μ,σ)+pF(x;μ,σc),

respectively.