Explicit estimators of the location and scale parameters of a symmetric hyperbolic distribution

Abstract

Explicit modified maximum likelihood estimators ( MMLE ) of the location and scale parameters of a symmetric hyperbolic distribution are obtained as linear functions of the order statistics of a random sample. These new estimators are unbiased and have some other nice properties. Numerical comparisons with respect to bias and mean squared error of MMLEs, moment estimators, MLEs, least square estimators and asymptotically most efficient estimators have been carried out.