Evaluation of probability point estimate methods.

*(English)*Zbl 0820.62088Summary: In modern engineering designs and analysis, computer models are frequently used. Due to the presence of uncertainties associated with the model inputs and parameters, which are treated as random variables, analysis is feasible if the methods employed do not require excessive computations yet produce reasonably accurate results. Point estimate methods are such schemes that are potentially capable of achieving the goals. Assuming normal distributions of the random variables, three point estimate methods [E. Rosenblueth, Proc. Natl. Acad. Sci. USA 72, 3812-3814 (1975; Zbl 0319.62027), Appl. Math. Modelling 5, 329-335 (1981; Zbl 0478.65088); M. E. Harr, ibid. 13, 313-318 (1989), and a modified Harr’s method] were evaluated in this paper for different numbers of random variables and different model types. Results of this evaluation indicated that the proposed modified Harr’s method yielded comparable, if not better, performance than the other two methods. Also, performance evaluation indicated that additional statistical information, other than the commonly used first two moments, should be incorporated, if available, to enhance the accuracy of uncertainty analysis.

##### MSC:

62N99 | Survival analysis and censored data |

65C99 | Probabilistic methods, stochastic differential equations |

62F10 | Point estimation |

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\textit{C.-H. Chang} et al., Appl. Math. Modelling 19, No. 2, 95--105 (1995; Zbl 0820.62088)

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