No abstract

In many engineering and scientific problems, there is a need to find the parameters of a dependence from the experimental data. There exist several software packages that find the values for these parameters -values for which the mean square value of the absolute approximation error is the smallest. In practice, however, we are often interested in minimizing the mean square value of the relative approximation error. In this paper, we show how we can use the absolute-error-minimizing software to minimize the relative error.

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A natural way to estimate the probability density function of an unknown distribution from the sample of data points is to use histograms. The accuracy of the estimate depends on the size of the histogram's bins. There exist heuristic rules for selecting the bin size. In this paper, we show that these rules indeed provide the optimal value of the bin size.

One of the possible ways of dealing with interval uncertainty is to use Monte-Carlo simulations. A recent study of using this technique for the analysis of different smart electric grid-related algorithms shows that we need approximately 500 simulations to compute the corresponding interval range with 5% accuracy. In this paper, we provide a theoretical explanation for these empirical results.