Characterization of tails through hazard rate and convolution closure   properties
  We use the properties of the Matuszewska indices to show asymptotic inequalities for hazard rates. We discuss the relation between membership in the classes of dominatedly or extended rapidly varying tail distributions and corresponding hazard rate conditions. Convolution closure is established for the class of distributions with extended rapidly varying tails. 
Anastasios G. Bardoutsos and Dimitrios G. Konstantinides
math.PR