A simple estimator for the characteristic exponent of the stable Paretian distribution

A new estimator for the index α of symmetric stable Paretian distributions is proposed. In addition to being numerically simple, fast, and reliable, simulations suggest that even in small samples, the estimator is unbiased for α ∈ [1, 2], and almost exactly normally distributed. Standard errors are also given, the magnitudes of which are shown to depend only on sample size and not on the true value of α.