The generalized two-sided beta distribution with applications in project risk analysis. (English) Zbl 1517.62056
Summary: A novel smooth, three-parameter, asymmetric two-sided distribution with bounded support is constructed via a half-symmetric beta distribution. Denoting that novel asymmetric distribution the generalized two-sided beta (GTSB) distribution, it is characterized by a mode (or anti-mode) parameter together with two branch power parameters. GTSB distributions serve as a smooth alternative for generalized two-sided power distributions. Some properties of the GTSB family of distributions shall be derived. Two separate algorithms to solve for the power parameters of the GTSB distribution shall be presented. The first algorithm ensures matching of the most likely value, specified through expert judgment, as well as the PERT mean and PERT variance, popular in project management. The latter result is a novel PERT contribution by itself. The second algorithm solves for the power parameters from a lower and upper quantile constraint. The application of the GTSB distribution shall be demonstrated in illustrative PERT example(s).
MSC:
| 62E10 | Characterization and structure theory of statistical distributions |
| 62E15 | Exact distribution theory in statistics |
| 90B50 | Management decision making, including multiple objectives |
| 90B35 | Deterministic scheduling theory in operations research |
| 91B84 | Economic time series analysis |
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