Limiting behaviour of constrained sums of two variables and the principle of a single big jump

作者：Lehtomaa Jaakko^*

来源：Statistics & Probability Letters, 2015, 107: 157-163.

DOI：10.1016/j.spl.2015.08.017

• Principle of a single big jump
• Log-convex
• Increasing failure rate
• Heavy-tailed

This note studies the asymptotic properties of the variable Z(d) := x(1)/d vertical bar {X-1 + X-2 = d}, as d -> infinity. Here X-1 and X-2 are non-negative i.i.d. variables with a common twice differentiable density function f. General results concerning the distributional limits of Z(d) are discussed with various examples.

• 出版日期2015-12