Some estimates of the normal approximation for mixture of Poisson and gamma random variables

Abstract

In the paper, we present the upper bound of L_p norms ∆_p of the order (a₁ + a₂)/(DZ)^-1/2 for all 1 < p< ∞, of the normal approximation for a standardized random variable (Z - EZ)/√DZ, where the random variable Z = a₁X + a₂Y , a₁ + a₂ = 1, a_i > 0, i = 1, 2, the random variable X is distributed by the Poisson distribution with the parameter λ > 0, and the random variable Y by the standard gamma distribution Γ (α, 0, 1) with the parameter α > 0.