Some equivalent conditions of one class of heavy-tailed distributions;

Influence of heavy-tailed distribution on network traffic

The estimation of tail index for regular variation heavy-tailed distributions aroused our concern,many scholars proposed several methods,but all of them have some disadvantages.

They are precise large deviations for the aggregate claim amount process with heavy-tailed distributions, the Cramer-Lundberg approximation property and the Lundberg inequality for the ruin functions under the corresponding risk models.

Since many estimation methods of tail index for heavy tailed distribution turned out to have limitations,Crovella proposed a new method with which tail index can be estimated in terms of scaling properties.

In this paper,the self-similar traffic generated by multiplexing the ON/OFF points which meet the Pareto heavy-tail distribution is discussed.

Laevens’ formula of PSD and TAM method, and puts forward the TAM method for calculating the PSD of heavy-tailed ON/OFF source.

Nagaev and Heyde, many scholars deeply studied the large deviations for heavy-tailed random variables.

They are ND with heavy-tailed distribution for ruin probability.

In order to meet the needs of recent research in applied probability, in this paper the concepts of heavily heavy-tailed distribution and lightly heavy-tailed distribution are introduced.