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Inference for double Pareto lognormal queues with applications

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  • Ramírez Cobo, Josefa
  • Lillo Rodríguez, Rosa Elvira
  • Wiper, Michael Peter
  • Wilson, Simon P.

Abstract

In this article we describe a method for carrying out Bayesian inference for the double Pareto lognormal (dPlN) distribution which has recently been proposed as a model for heavy-tailed phenomena. We apply our approach to inference for the dPlN/M/1 and M/dPlN/1 queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not posses a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform for the Pareto/M/1 system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.

Suggested Citation

  • Ramírez Cobo, Josefa & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter & Wilson, Simon P., 2008. "Inference for double Pareto lognormal queues with applications," DES - Working Papers. Statistics and Econometrics. WS ws080402, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws080402
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    References listed on IDEAS

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    1. John F. Shortle & Martin J. Fischer & Percy H. Brill, 2007. "Waiting-Time Distribution of M/D N /1 Queues Through Numerical Laplace Inversion," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 112-120, February.
    2. Ausín Olivera, María Concepción & Lillo Rodríguez, Rosa Elvira & Wiper, Michael Peter, 2004. "Bayesian control of the number of servers in a GI/M/c queuing system," DES - Working Papers. Statistics and Econometrics. WS ws046917, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Carl M. Harris & William G. Marchal, 1998. "Distribution Estimation Using Laplace Transforms," INFORMS Journal on Computing, INFORMS, vol. 10(4), pages 448-458, November.
    4. John F. Shortle & Percy H. Brill & Martin J. Fischer & Donald Gross & Denise M. B. Masi, 2004. "An Algorithm to Compute the Waiting Time Distribution for the M/G/1 Queue," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 152-161, May.
    5. Carl M. Harris & Percy H. Brill & Martin J. Fischer, 2000. "Internet-Type Queues with Power-Tailed Interarrival Times and Computational Methods for Their Analysis," INFORMS Journal on Computing, INFORMS, vol. 12(4), pages 261-271, November.
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    Heavy tails;

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