Saddlepoint Approximation for Sample Quantiles with Some Applications

Abstract

In this article, we use the integral form of the binomial distribution to derive saddlepoint approximations for sample quantiles. As an application, we present the calculation of the tail probability of the empirical log-likelihood ratio statistic for quantiles. Simulation results are also given to show that our approximations are extremely accurate.

Keywords:

• Empirical likelihood
• Saddlepoint approximation
• Sample quantile

Mathematics Subject Classification:

• Primary 62E20
• Secondary 62G30

Acknowledgment

The authors would like to thank a referee for his/her comments and criticisms which helped to improve the article a great deal.