Journal of Data Science

The shape parameter of a symmetric probability distribution is often more difficult to estimate accurately than the location and scale parameters. In this paper, we suggest an intuitive but innovative matching quantile estimation method for this parameter. The proposed shape parameter estimate is obtained by setting its value to a level such that the central 1-1/n portion of the distribution will just cover all n observations, while the location and scale parameters are estimated using existing methods such as maximum likelihood (ML). This hybrid estimator is proved to be consistent and is illustrated by two distributions, namely Student-t and Exponential Power. Simulation studies show that the hybrid method provides reasonably accurate estimates. In the presence of extreme observations, this method provides thicker tails than the full ML method and protect inference on the location and scale parameters. This feature offered by the hybrid method is also demonstrated in the empirical study using two real data sets.