Застосування непараметричних методів до статистичного оцінювання вибіркових характеристик
Journal Title: Математичне моделювання - Year 2016, Vol 1, Issue 2
Abstract
APPLICATION OF NONPARAMETRIC METHODS TO STATISTICAL EVALUATION OF THE CHARACTERISTICS OF THE SAMPLE Stroyevа V.O., Nakopia M. Abstract Mathematical modeling has been widespread in various fields of science: mechanics, physics, statistics, medicine, biology, including in ecology. Many of these tasks are related to the processing of data by the method of statistical research. The observation processing by parametric methods is based on a number of a priori assumptions such as the independence of measurements and their errors, uniformity of dispersions, normality of distribution, and so on. Possible deviations from these assumptions, for example, for environmental data, can seriously affect the validity of the final conclusions. Therefore, a modern alternative to parametric methods is the simulation of empirical data distribution using repeat generation methods (numerical resampling). These technologies do not require any a priori information about the law of distribution of the investigated random variable. Instead, they perform multiple processing of different empirical data. In ecology, it is possible to cut data only in a certain place and at a certain point in time, and if you select a second, third sample, etc., then it will already be data from another place or taken at another time. So, how, having only one single repeat, to evaluate the value of the indicator we need and get the measure of the accuracy of this estimate? At the same time, the exact type of distribution of the processed data is usually not known, therefore, approximate methods of approximating the predicted properties of the investigated statistics are used. How the degree of this approximation affects the final conclusions, remains entirely on the conscience of the researcher. We can say that solving these problems can be done using methods of generation of repeated samples (numerical resampling), which relate to nonparametric methods. The purpose of this work is to develop and program the implementation of algorithms that allow solving special problems of statistical processing of data. Namely, on the basis of the investigated methods of numerical resampling algorithms for solving typical problems, which were then programmed implemented by means of speech R. The results of researches of mathematical models of ecological information systems for which algorithms of nonparametric statistics are used give answers to the questions asked and indicate that the developed algorithms can be applied to other classes of applied problems, which in their mathematical formula are similar to the ones presented. References [1] Nakopia M. Some cases of application of methods of numerical resampling in applied problems / M.Nakopia // Mathematical modeling, Dneprodzerzhinsk., №2(33) – 2015 –– С. 11–13. [2] Efron B. An intrduction to the bootstrap. / B. Efron, R.J.Tibshirani // N. Y.: Chapman &Hall – 1993 – Р. 436. [3] Manly B.F. Randomization, bootstrap and Monte Carlo methods in biology / B.F. Manly // London:Chapman & Hall – 2007 – Р. 445. [4] Anatoliev S. Fundamentals of Butterplating / S. Anatoliev // Quantile – 2007 – №3 – С. 1–12. [5] Shitikov V.K. Randomization and bootstrap: statistical analysis in biology and ecology with use of R / V.K.Shitikov, G.S. Rosenberg // Togliatti: Cassandra – 2013 – С. 314.
Authors and Affiliations
В. О. Строєва, М. Накопія
Keywords
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