We present a visual, interactive method for specifying a bounded Johnson (SB) probability distribution when little or no data are available for formally identifying and fitting an input process. Using subjective information, the modeler provides values for familiar characteristics of an envisioned target distribution. These numerical characteristics are transformed into parameter values for the probability density function. The parameters can then be indirectly manipulated, either by revising the desired numerical values of the function's specifiable characteristics or by directly altering the shape of the displayed curve. Interaction with a visual display of the fitted density permits the modeler to conveniently obtain a more realistic representation of an in put process than was previously possible. The techniques involved have been packaged into a public-domain microcomputer-based software system called VISIFIT.
Beach, L.R. and Swenson, R.G. (1966). Intuitive estimation of means. Psychon. Sci.5, 161-162.
2.
Beasley, J.D. and Springer, S.G. (1977). The percentage points of the normal distribution . Applied Statistics26, 118-121.
3.
Burr, I.W. (1973). Parameters for a general system of distributions to match a grid of α3 and α4. Comm. Statist.2, 1-21.
4.
Conway, R.; Maxwell, W.L; McClain, J.O. and Worona, S.L. (1987). User's Guide to XCELL+Factory Modeling System , 2nd Ed. The Scientific Press , Redwood City, Calif.
5.
Dew, P.M. and James, K.R. (1983). Introduction to Numerical Computation In Pascal . Springer-Verlag New York Inc., New York.
6.
Doubilet, P.; Begg, C.B.; Weinstein, M.C.; Braun, P. and McNeil, B.J. (1985). Probabilistic sensitivity analysis using Monte Carlo simulation, a practical approach. Medical Decision Making5, 157-177.
7.
Hahn, G.J. and Shapiro, S.S. (1967). Statistical Models in Engineering. John Wiley and Sons, New York.
8.
Hill, I.D.; Hill, R. and Holder, R.L. (1976). Algorithm AS 99, fitting Johnson curves by moments . Applied Statistics25, 171-182.
9.
Johnson, M.E. (1987). Modeling and generating input processes. In: Proceedings of the 1987 Winter Simulation Conference (Thesen, A.; Grant, H. and Kelton, W.D.; eds.). Institute of Electrical and Electronics Engineers, San Francisco, California, 30-32.
10.
Johnson, N.L. (1949a). Systems of frequency curves generated by methods of translation. Biometrika36, 149-176.
11.
Johnson, N.L. (1949b). Bivariate distributions based on simple translation systemsBiometrika36, 297-304.
12.
Johnson, N.L. and Kotz, S. (1970). Continuous Univariate Distributions-1. John Wiley and Sons, New York.
13.
Kahneman, D.; Slovic, P. and Tversky, A. (1982). judgement under uncertainty: Heuristics and biases . Cambridge University Press.
14.
Lathrop, R.G. (1967). Perceived Variability. Journal of Experimental Psychology73, 498-502.
15.
Law, A.M. and Kelton, W.D. (1982). Simulation Modeling and AnalysisMcGraw-Hill Book Company, New York.
16.
Law, A.M. and Vincent, S.G. (1987. A Tutorial on UNIFIT, an Interactive Package for Fitting Probability Distributions to Observed Data. In: Proceedings of the 1987 Winter Simulation Conference ( Thesen, A.; Grant, H.; and Kelton, W.D.; eds.). Insitute of Electrical and Electronics Engineers, San Francisco, California, 217-221.
17.
Mage, D.T. (1980). An explicit solution for SB parameters using four percentile pointsTechnometrics22, 247-251.
18.
Microsoft Corporation, Microsoft C 5.0 Optimizing Compiler, Redmond, Washington.
19.
Nelder, J.A. and Mead, R. (1965). A simplex method for function minimization. The Computer Journal7, 308-313.
20.
Olsson, D.M. (1974). A sequential simplex program for solving minimization problems. Journal of Quality Technology6, 53-57.
21.
Peterson, C.R. and Miller, A. (1964). Mode, median, and mean as optimal strategies. Journal of Experimental Psychology68, 363-367.
22.
Ramberg, J.S. and Schmeiser, B.W. (1972). An approximate method for generating symmetric random variables. Comm. ACM15, 987-990.
23.
Ramberg, J.S. and Schmeiser, B.W. (1974). An approximate method for generating symmetric random variables. Comm. ACM17, 78-82.
24.
Roberts, S.D. (1983). Simulation ModelingandAnalysis with INSIGHT. Regenstrief Institute for Health Care, Indianapolis, Indiana.
25.
Schmeiser, B.W. and Deutsch, S.J. (1977). A versatile family of probability distributions suitable for simulation. AIIE Transactions9, 176-182.
Spencer, J. (1963). A further study of estimating averages. Ergonomics6, 255-265.
28.
Stroud, A.H. and Secrest, D. (1966). Gaussian Quadrature Formulas. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
29.
Swain, J.J.; Venkatraman, S. and Wilson, J.R. (1988). Least-squares estimation of distribution functions in Johnson's translation system. Journal of statistical Computation and Simulation29, 271-297.
30.
Tukey, J.W. (1960). The Practical Relationship Between the Common Transformations of Percentages of Counts and of Amounts. Technical Report 36, Statistical Techniques Research Group, Princeton University .
