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The maximum and sum of two beta variables and the analysis of PERT networks

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  • Sculli, D
  • Wong, KL

Abstract

This paper explores the errors involved in the approximation of both the maximum and sum of two independent Beta random variables, each by another Beta random variable. The principal area of application is the time analysis of PERT networks, and the results are interpreted and discussed in terms of this application. The error was found to be acceptable for the greater part of the range of the parameters involved. The results will help practitioners estimate the mean and standard deviation of the completion time of PERT networks.

Suggested Citation

  • Sculli, D & Wong, KL, 1985. "The maximum and sum of two beta variables and the analysis of PERT networks," Omega, Elsevier, vol. 13(3), pages 233-240.
    • Handle: RePEc:eee:jomega:v:13:y:1985:i:3:p:233-240
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    Cited by:

    1. Dawson, C. W., 1995. "A dynamic sampling technique for the simulation of probabilistic and generalized activity networks," Omega, Elsevier, vol. 23(5), pages 557-566, October.
    2. Pérez, José García & Martín, María del Mar López & García, Catalina García & Sánchez Granero, Miguel Ángel, 2016. "Project management under uncertainty beyond beta: The generalized bicubic distribution," Operations Research Perspectives, Elsevier, vol. 3(C), pages 67-76.
    3. Yousry Abdelkader, 2010. "Adjustment of the moments of the project completion times when activity times are exponentially distributed," Annals of Operations Research, Springer, vol. 181(1), pages 503-514, December.
    4. Saralees Nadarajah & Xiao Jiang & Jeffrey Chu, 2015. "A saddlepoint approximation to the distribution of the sum of independent non-identically beta random variables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(2), pages 102-114, May.
    5. Yousry Abdelkader, 2010. "Computing the moments of order statistics from independent nonidentically distributed Beta random variables," Statistical Papers, Springer, vol. 51(2), pages 307-313, June.
    6. Mohammad Ghaderi, 2020. "Public Health Interventions in the Face of Pandemics: Network Structure, Social Distancing, and Heterogeneity," Working Papers 1193, Barcelona School of Economics.
    7. Ghaderi, Mohammad, 2022. "Public health interventions in the face of pandemics: Network structure, social distancing, and heterogeneity," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1016-1031.
    8. Saraless Nadarajah, 2006. "Exact and approximate distributions for the product of inverted Dirichlet components," Statistical Papers, Springer, vol. 47(4), pages 551-568, October.
    9. Mohammad Ghaderi, 2020. "Public health interventions in the face of pandemics: network structure, social distancing, and heterogeneity," Economics Working Papers 1732, Department of Economics and Business, Universitat Pompeu Fabra.

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