On Asymptotic Behavior of Regularly Varying Moments for Discrete Laws

Abstract

For a discrete law F and large n, we investigate the asymptotic relation

where ℓ(·) is an arbitrary slowly varying function. Then we prove that regularly varying moments for Power Series Distributions, generated by an entire function of finite order, satisfy the above relation with C _μ = 1 for each μ ∈ (0, ∞).

Keywords:

• Entire functions of finite order
• Power series distributions
• Regular variation

Mathematics Subject Classification:

• 60E05
• 26A12