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An estimator for the $\M$-index of functions of $\mathcal{M}$, a larger classthan the class of regularly varying (RV) functions, is proposed. This index isthe tail index of RV functions and this estimator is thus a new one on theclass of RV functions. This estimator satisfies, assuming suitable conditions,strong consistency. Asymptotic normality of this estimator is proved for alarge class of RV functions, showing a better performance than some well-knownestimators. Illustrations with simulated and real life datasets are provided.

A simple estimator for the $\mathcal{M}$-index of functions in $\mathcal{M}$