Abstract
In reliability safety analysis of civil engineering systems, we encounter parameters which are generally bounded and skewed random quantities. Exemplifying these parameters are factors of safety or safety indexes, variables representing strength of materials, intensity of loads, etc. Harr (1977) demonstrated the ability of the beta (or Pearson type 1) distribution to approximate most of the geotechnical parameters. Obini and Bourdeau (1985) simplified use of the beta distribution and investigated its sensitivity to the bound locations. Fielitz and Myers (1975) argued for the method of moments (MOM) to estimate the parameters of the beta distribution for ease of computation. Romesburg (1976) commented that formulation of the problem in terms of smallest order statistics would allow the use of the method of maximum likelihood estimation (MLE) to estimate the parameters of the beta distribution with little more effort than MOM. In multivariate cases, however, MOM would be the only practical method for parameter estimation.
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References
Fielitz, B.D. and Myers, B.L., 1975. Estimation of parameters in the beta distribution. Decision Sciences, Vol. 6, No. 1, pp. 1–13.
Gnanadeshikan, R., Pinkham, R.S. and Hughes, L.P., 1967. Maximum likelihood estimation of the beta distribution from smallest order statistics. Technometrics, Vol. 9, No. 4, pp. 67–620.
Harr, M.E., 1977. Mechanics of Particulate Media: A Probabilistic Approach. McGraw-Hill Book Company, New York.
Oboni, F. and Bourdeau, P.L., 1985. Simplified use of the beta distribution and sensitivity to bounded locations. Structural Safety, Vol. 3, pp. 63–66.
Romesburg, H.C., 1976. Estimation of parameters in the beta distribution: Comment. Decision Sciences, Vol. 7, pp. 162.
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© 1998 Springer Science+Business Media Dordrecht
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Singh, V.P. (1998). Beta Distribution. In: Entropy-Based Parameter Estimation in Hydrology. Water Science and Technology Library, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1431-0_16
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DOI: https://doi.org/10.1007/978-94-017-1431-0_16
Publisher Name: Springer, Dordrecht
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