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Beta Distribution

The Beta Distribution is a continuous distribution that has both upper and lower finite bounds.

Because many real situations can be bounded in this way, the Beta distribution can be used empirically to estimate the actual distribution before much data is available. Even when data is available, this distribution should fit most data in a reasonable fashion, although it may not be the best fit.

Beta distribution used in business process simulation beta distribution used in process simulation
beta distribution used in process simulation software beta distribution used in process improvement.

As can be seen in the examples above, This distribution can approach zero or infinity at either of its bounds, with p controlling the lower bound and q controlling the upper bound. Values of p,q<1 cause the Beta distribution to approach infinity at that bound. Values of p,q>1 cause the Beta distribution to be finite at that bound.

Beta distributions have many, many uses such as to model distributions of hydrologic variables, logarithm of aerosol sizes, activity time in PERT analysis, isolation data in photovoltaic system analysis, porosity / void ratio of soil, phase derivatives in communication theory, size of progeny in Escherchia Coli, dissipation rate in breakage models, proportions in gas mixtures, steady-state reflectivity, clutter and power of radar signals, construction duration, particle size, tool wear, and others. Many of these uses occur because of the doubly bounded nature of the Beta distribution.

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About the Author:

Scott Baird has been president of ProcessModel for more than 15 years. His focus has been to teach others how to improve processes dramatically. He has been successful in transferring these skills to over 200 companies, including ESPN, NASA, GE, Nationwide, Cendant, SSA and many more. Specialties: Group facilitation for process improvement, process design and simulation, simulation modeling, business management and training others to see opportunities. Scott loves to teach process improvement and has often been heard to say, “Of all the things I do, training others to improve processes is my favorite.” Scott is a father of four and a grandfather of eight. He is an avid woodworker, designing and creating presentation boxes. In his spare time, he volunteers in a college preparation program.