Stochastic optimization problem is, as a rule, formulated in terms of expected cost function. However, the criterion based on averaging does not take in account possible variability of involved random variables. That is why the criterion considered in the present contribution uses selected quantiles. Moreover, it is assumed that the stochastic characteristics of optimized system are estimated from the data, in a non-parametric setting, and that the data may be randomly right-censored. Therefore, certain theoretical results concerning estimators of distribution function and quantiles under censoring are recalled and then utilized to prove consistency of solution based on estimates. Behavior of solutions for finite data sizes is studied with the aid of randomly generated example of a newsvendor problem.
Conclusions: The present paper was not aimed at reviewing existing NLTE prominence models, but rather to show
schematically ihe existing problems connected with such a models. There was no space to discuss the importance of plasma parameter determination for prominence MHD-modeling - for some particular questions see other reviews mentioned in this paper. Another interesting problem is the presence of oscillations (Suematsu et al., 1990). We should also stress that the present discussion was restricted only to stationary models, assuming that all atomic relaxations are much more rapid as compared to temporal variations of the plasma thermodynamic structure. In fact, for low hydrogen densities radiative recombination relaxatíon takes a rather long time (up to several tens of seconds - see Heinzel, 1991), which is to be compared to the typical life-time of prominence fine structures (Engvold, 1980). NLTE modeling of
temporal variations of prominence fine structures is an important new challenge and should be done simultaneously with new multiline observations in the UV (SOHO-mission), optical and IR (THEMIS) wavelength regions, made with sufficient spatial, spectral and temporal resolution.