On the convolution of Pareto and gamma distributions |
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| Affiliation: | 1. School of Mathematics, University of Manchester, Manchester M60 1QD, United Kingdom;2. Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, United States;1. Department of Informatics, Karlsruhe Institute of Technology, Germany;2. Siemens Corporation, Corporate Technology, Princeton, NJ, USA;3. Federal University of Rio de Janeiro (UFRJ), PO BOX 68.530, 21941-590 Rio de Janeiro/RJ, Brazil;4. Federal University of the State of Rio de Janeiro, RJ, Brazil;5. Duke University, Durham, NC, USA;1. Department of Statistics, Columbia University, 1255 Amsterdam Avenue, New York, NY, 10027, USA;2. Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong;1. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, Zhejiang Province, China;2. Department of Applied Finance and Actuarial Studies, Macquarie University, NSW, Australia |
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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. |
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