  Here we suppose that the observed random variable has cumulative distribution
function $F$ with regularly varying tail, i.e. $1-F \in RV_{-\alpha}$, $\alpha
> 0$. Using the results about exponential order statistics we investigate
logarithms of ratios of two order statistics of a sample of independent
observations on Pareto distributed random variable with parameter $\alpha$.
Short explicit formulae for its mean and variance are obtained. Then we
transform this function in such a way that to obtain unbiased, asymptotically
efficient, and asymptotically normal estimator for $\alpha$. Finally we
simulate Pareto samples and show that in the considered cases the proposed
estimator outperforms the well known Hill, t-Hill, Pickands and
Deckers-Einmahl-de Haan estimators.
