The generalized two-sided power distribution

Abstract

The generalized standard two-sided power (GTSP) distribution was mentioned only in passing by Kotz and van Dorp Beyond Beta, Other Continuous Families of Distributions with Bounded Support and Applications, World Scientific Press, Singapore, 2004. In this paper, we shall further investigate this three-parameter distribution by presenting some novel properties and use its more general form to contrast the chronology of developments of various authors on the two-parameter TSP distribution since its initial introduction. GTSP distributions allow for J-shaped forms of its pdf, whereas TSP distributions are limited to U-shaped and unimodal forms. Hence, GTSP distributions possess the same three distributional shapes as the classical beta distributions. A novel method and algorithm for the indirect elicitation of the two-power parameters of the GTSP distribution is developed. We present a Project Evaluation Review Technique example that utilizes this algorithm and demonstrates the benefit of separate powers for the two branches of activity GTSP distributions for project completion time uncertainty estimation.

Keywords:

• Parameter elicitation
• moment ratio diagram
• PERT technique

Acknowledgements

We are indebted to Samuel Kotz who has been very gracious in donating his time to provide comments and suggestions in the development of this paper. The authors are thankful to the referee and the editor of the Journal of Applied Statistics whose valuable comments significantly improved the contents and presentation of an earlier version.

Notes

Kamburowski 10 notes that: ‘Despite the criticisms and the abundance of new estimates, the PERT mean and variance [given by (26) in this paper] can be found in almost every textbook on OR/MS and P/OM, and are employed in much project management software’.