RESEARCH OF SIMULATION OF ONE-DIMENSIONAL SAMPLES USING POLYNOMIAL SPLINES

Abstract

The use of modeling to solve various problems is due to a set of reasons: saving time and material resources, simulation of “critical” modes, which in real operation can be dangerous for the object under study, the possibility of distance learning and others. In particular, modeling not the operation of a system, but data sequences of a certain type could solve the problem of lack of such data (for example, in machine learning), which is relevant especially in the case of working in multidimensional spaces. When simulating samples, the first thing to start from is the distribution model to be obtained. The model can be determined by some analytical law of distribution (normal, Weibull, uniform, etc.), and in this it depends on the parameters (parametric model). Models are usually chosen so that their parameters carry some meaningful interpretation (a, b – the beginning and end of the interval in a uniform distribution, λ – intensity in exponential, etc.). Another class of models that reproduce distribution functions are nonparametric (nuclear methods, histogram estimates of the empirical distribution function, spline approximation). The main problem with parameterbased methods is limited, especially in two cases: 1. When modeling multidimensional data – in this case, the work always leads to a transition to multidimensional normal distribution. 2. When modeling inhomogeneous samples, which are a mixture of several distributions (not necessarily from one class), truncated or those that contain gaps in observations. In this context, the use of parametric models is objectively impossible in its purest form. Therefore, the presence of a tool that well approximates inhomogeneous data is desirable to solve the problem of generating inhomogeneous multidimensional sets.