On the convolution of Pareto and gamma distributions

  • Authors:
  • Saralees Nadarajah;Samuel Kotz

  • Affiliations:
  • School of Mathematics, University of Manchester, Manchester M60 1QD, United Kingdom;Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, United States

  • Venue:
  • Computer Networks: The International Journal of Computer and Telecommunications Networking
  • Year:
  • 2007

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Abstract

It is well established that the burst and idle times for on/off traffic are modeled by the Pareto and gamma distributions, respectively. Thus, the inter arrival times between on-traffic (off-traffic) is the convolution of Pareto and gamma random variables. In this note, we derive exact expressions for the probability density function of the inter arrival times. A computer program and tabulations of the associated percentage points are also provided.