TECHNICAL PAPERS
Dec 1, 1991

Visual Interactive Fitting of Beta Distributions

Publication: Journal of Construction Engineering and Management
Volume 117, Issue 4

Abstract

This paper describes a visual interactive procedure for fitting beta distributions to activity times in a simulation model when sample data are not available for statistical analysis of the model's input processes. Using subjective information about a given activity time the modeler specifies the activity's minimum and maximum times together with two of the following characteristics: mode, mean, variance, or selected percentiles. The fitting procedure includes efficient methods for computing the shape parameters of the beta distribution that most nearly matches the specified characteristics. The user can manipulate the fitted distribution by either revising the specified characteristics or directly altering a visual display of the density. This fitting procedure was implemented in a public‐domain microcomputer‐based software system called VIBES (visual interactive beta estimation system). An example from construction engineering illustrates the operation of VIBES.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
AbouRizk, S. M. (1989). VIBES user's guide. Division of Construction Engineering and Management, Purdue University, West Lafayette, Ind.
2.
AbouRizk, S. M. (1990). “Input modeling for construction simulation,” thesis presented to Purdue University, at West Lafayette, Ind., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
3.
AbouRizk, S. M., Halpin, D. W., and Wilson, J. R. (1990). “Modeling input data with the beta distribution—a description of the BetaFit software.” Division of Construction Engineering and Management, Purdue University, West Lafayette, Ind.
4.
Alpert, M., and Raiffa, H. (1982). “A progress report on the training of probability assessors.” Judgment under uncertainty: Heuristics and biases, D. Kahneman, P. Slovic, and A. Tversky, eds., Cambridge University Press, Cambridge, England.
5.
Beach, L. R., and Swenson, R. G. (1966). “Intuitive estimation of means.” Psychonomic Sci., 5(4), 161–162.
6.
Conte, S. D., and de Boor, C. (1980). Elementary numerical analysis: An algorithmic approach. McGraw‐Hill Book Co., Inc., New York, N.Y.
7.
Debrota, D. J., Dittus, R. S., Roberts, S. D., and Wilson, J. R. (1989). “Visual interactive fitting of bounded Johnson distributions.” Simulation, 52(5), 199–205.
8.
Fowler, H. W., and Fowler, F. G. (1931). The king's English. 3rd Ed., Oxford University Press, Oxford, England.
9.
Griffiths, P., and Hill, I. D. (1985). Applied statistics algorithms. Royal Statistical Society, London, England.
10.
Grubbs, F. E. (1962). “Attempts to validate certain PERT statistics or ‘picking on PERT,’” Operations Res., 10(2), 912–915.
11.
Johnson, N. L., and Kotz, S. (1970). Distributions in statistics: Continuous univariate distributions—1. John Wiley and Sons, Inc., New York, N.Y.
12.
Klein, R. W., and Baris, P. M. (1991). “Selecting and generating variates for modeling service times.” Computers and Industrial Engineering, 20(1), 27–33.
13.
Lathrop, R. G. (1967). “Perceived variability.” J. Experimental Psychology, 73(4), 498–502.
14.
Lichtenstein, S., Fischhoff, B., and Phillips, L. D. (1982). “Calibration of probabilities: The state of the art to 1980.” Judgment under uncertainty: Heuristics and biases, D. Kahneman, P. Slovic, and A. Tversky, eds., Cambridge University Press, Cambridge, England.
15.
MacCrimmon, K. R., and Ryavec, C. A. (1964). “An analytical study of the PERT assumptions.” Operations Res., 12(1), 16–37.
16.
McBride, W. J., and McClelland, C. W. (1967). “PERT and the beta distribution.” IEEE Trans. on Engrg. Mgmt., EM‐14(4), 166–169.
17.
Microsoft QuickBASIC programmer's guide. (1989). Microsoft Corporation, Redmond, Wash.
18.
Olsson, D. M. (1974). “A sequential simplex program for solving minimization problems.” J. Quality Tech., 6(1), 53–57.
19.
Peterson, C., and Miller, A. (1964). “Mode, median, and mean as optimal strategies.” J. Experimental Psychology, 68(4), 363–367.
20.
QuickPak professional—advanced programming library for BASIC compilers, version 3.0. (1989). Crescent Software, Stamford, Conn.
21.
Spencer, J. (1963). “A further study of estimating averages.” Ergonomics, 6, 255–265.
22.
van Leunen, M.‐C. (1986). A handbook for scholars. Alfred A. Knopf, Inc., New York, N.Y.
23.
Wilson, J. R., Vaughan, D. K., Naylor, E., and Voss, R. G. (1982). “Analysis of Space Shuttle ground operations.” Simulation, 38(6), 187–203.

Information & Authors

Information

Published In

Go to Journal of Construction Engineering and Management
Journal of Construction Engineering and Management
Volume 117Issue 4December 1991
Pages: 589 - 605

History

Published online: Dec 1, 1991
Published in print: Dec 1991

Permissions

Request permissions for this article.

Authors

Affiliations

Simaan M. AbouRizk, Associate Member, ASCE
Asst. Prof., Dept. of Civ. Engrg., Univ. of Alberta, Edmonton, Alberta, T6G 2G7, Canada
Daniel W. Halpin, Member, ASCE
Prof. and Head, Div. of Constr. Engrg. and Mgmt., Purdue Univ., West Lafayette, IN 47907
James R. Wilson
Assoc. Prof., School of Industrial Engrg., Purdue Univ., West Lafayette, IN

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share