Some estimates of the normal approximation for mixture of Poisson and gamma random variables - Sunklodas, Jonas Kazys (Lietuvos matematikos rinkinys, 2010)
In the paper, we present the upper bound of Lp 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, ai > 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.