1b1d6acc-aa14-4579-92f1-72add0e23dd220210222115815944wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS1109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185Numerical Computation of the Small Balls Probability for RandomFunctions with Normal ComponentsJiříZelinkaDepartment of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno, CZECH REPUBLICStatistical methods are often based on the properties of the distribution of random variables or randomvectors. In functional data analysis (FDA) we do not work with random observation containing a finite randomvector, but the whole function is one observation. We call it the functional random variable or the randomfunction, in short. This paper offers the possibility to generate random functions with normal components. In thiscase, the probability of small balls can be calculated numerically using the characteristic function. This tool canbe very useful in simulations and testing various kinds of estimates.92520209252020458462https://www.wseas.org/multimedia/journals/mathematics/2020/a965106-046.pdf10.37394/23206.2020.19.48https://www.wseas.org/multimedia/journals/mathematics/2020/a965106-046.pdfFerraty, F. ed.:Recent Advances in Functional Data Analysis and Related Topics. Springer Science & Business Media, ISBN 3-790-82736-3 (2011).10.1007/s00180-008-0111-2Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer Series in Statistics, Springer, New York. ISBN: 0-387-30369-3 (2006).NPFDAwebpage:https://www.math.univ-toulouse.fr/staph/npfda/Rudin, W.: Real and Complex Analysis. Mc-Graw Hill (1970)Ushakov, N.G.: Selected Topics in Characteristic Functions, De Gruyter, ISBN: 9-067-64307-6 (1999).10.1007/978-3-319-55846-2Zelinka J.: Random Functional Variable and Fourier Series. In: Aneiros G., Bongiorno E., Cao R., Vieu P. (eds) Functional Statistics and Related Fields. Contributions to Statistics. Springer, (2017).