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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 15
Edited by: B.H.V. Topping
Paper III.3

Computing Pearson - III Statistics

P.H. McDonald

Department of Civil Engineering, North Carolina State University, Raleigh, United States of America

Full Bibliographic Reference for this paper
P.H. McDonald, "Computing Pearson - III Statistics", in B.H.V. Topping, (Editor), "Developments in Civil & Construction Engineering Computing", Civil-Comp Press, Edinburgh, UK, pp 65-71, 1993. doi:10.4203/ccp.15.3.3
This paper analyzes the skewed data sample and frequency distribution known as Pearson Type III. The statistics for both sample and distribution are displayed, and the normalizing constant is computed. It is shown that this constant can be expressed as a complete Gamma Function, and an asymptotic series is utilized for its computation. An expression is developed for calculating the cumulative probability for the Pearson-III distribution, which proves to be practical using a recurrence relationship between the terms in its series expansion. Programs are displayed for these computations using Pascal source code. A numerical example accompanies the exposition. The example is taken from construction practice relative to pile driving. A simulation of a particular pile driving project is shown, and the statistics produced in a random number-generated distribution are compared with those of the sample.

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