Open AccessNumerical Computation of the Small Balls Probability for RandomFunctions with Normal Components
Author(s) -
Jiří Zelinka
Publication year - 2020
Publication title -
wseas transactions on mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.211
H-Index - 21
eISSN - 2224-2880
pISSN - 1109-2769
DOI - 10.37394/23206.2020.19.48
Subject(s) - random variable , computation , probability density function , normal distribution , probability distribution , statistical physics , mathematics , probability generating function , function (biology) , cumulative distribution function , random function , characteristic function (probability theory) , moment generating function , algorithm , computer science , distribution (mathematics) , statistical analysis , statistics , mathematical analysis , physics , evolutionary biology , biology
Statistical 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.