  Ratios of central order statistics seem to be very useful for estimating the
tail of the distributions and therefore, quantiles outside the range of the
data. In 1995 Isabel Fraga Alves investigated the rate of convergence of three
semi-parametric estimators of the parameter of the tail index in case when the
cumulative distribution function of the observed random variable belongs to the
max-domain of attraction of a fixed Generalized Extreme Value Distribution.
They are based on ratios of specific linear transformations of two extreme
order statistics. In 2019 we considered Pareto case and found two very simple
and unbiased estimators of the index of regular variation. Then, using the
central order statistics we showed that these estimators have many good
properties. Then, we observed that although the assumptions are different, one
of them is equivalent to one of Alves's estimators. Using central order
statistics we proved unbiasedness, asymptotic consistency, asymptotic normality
and asymptotic efficiency. Here we use again central order statistics and a
parametric approach and obtain distribution sensitive estimators of the index
of regular variation in some particular cases. Then, we find conditions which
guarantee that these estimators are unbiased, consistent and asymptotically
normal. The results are depicted via simulation study.
