Metamodels for Estimating Quantiles of Systems with One Controllable Parameter

We investigate the properties and robustness of histogram approximation to construct non-functional-form metamodels for estimating quantiles of systems with one controllable parameter, providing a general trend of quantiles. By non-functional-form metamodel, we mean the metamodel is not described by a single formula. The procedure constructs histograms by tracking sample quantiles at certain grid points. The algorithm dynamically increases the sample size so that the quantile estimates obtained via the histogram satisfy the proportional precision. The non-functional-form metamodel is constructed with a set of carefully selected histograms. Quantiles can then be estimated via the metamodel. An experimental performance evaluation demonstrates the validity of using non-functional-form metamodels to estimate quantiles.