R-Estimator of Location of the Generalized Secant Hyperbolic Distribution

ABSTRACT

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

Keywords:

• Cauchy distribution
• Hyperbolic secant distribution
• Rank estimators
• Rank tests

Mathematics Subject Classification:

• 62G10
• 62G32

Acknowledgment

The author would like to express her gratitude to Phil Pollett and Kaye Basford for their valuable comments. The author also thanks the anonymous referee for many constructive suggestions on this research.