2015/12/10 by S. Ravi, Ravi, Sreenivasan, Mandagere Chandrashekhar Manohar +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #60F10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1512.03186
openalex publication_date 2015/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a fixed positive integer k, limit laws of linearly normalized k-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized k-th upper order statistics under fixed and random sample sizes is carried out using tail equivalence which leads to some interesting tail behaviours of the limit laws. These lead to definitive answers about their max domains of attraction. Stochastic ordering properties of the limit laws are also studied. The results obtained are not dependent on linear norming and apply to power norming also and generalize some results already available in the literature. And the proofs given here are elementary.