WIT Press

Characteristic Value Determination For Arbitrary Distribution


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WIT Press


D. Zupan & G. Turk


This paper deals with the characteristic value determination from relatively small samples.When using samples the parameters of distribution can only be estimated and the correct characteristic value is unknown. The methods of estimation of characteristic values for several distributions and previously prescribed confidence intervals are presented in this paper. Results are confirmed by simulations. 1 Introduction In engineering practice the random variables are usually represented by their characteristic values. This approach is suitable for further analysis and design because we can use the fixed values without employing any probability methods. However, when only relatively small sample is available, the characteristic value is only estimated from that sample. The estimate is based on the assumption that the distribution of the variable is known and that its parameters are approximated from a sample. If we review the European standards [3] different distributions are usually prescribed for the determination of the resistance of different materials and for the determination of the resistance of structures: normal, lognormal, Gumbel, etc. For most cases formulae for the 75% confidence interval for the estimates of 5% characteristic values are prescribed. All the standards and the substandards propose the results in the form of tables of coefficients; without any analytical alternatives proposed. We in contrast analyze the problem in rather more general form. Our approach offers the confidence interval for the arbitrary characteristic value, which can be obtained analytically for some distributions. By the use of analytical formulae the tables, similar to those in European standards, are presented for the normal and lognormal distribution. For an arbitrary distribution an approximation