Statistical Convergence Of The Random Variables And Using Statistical Convergence To Deal With Data

Theory of Probability is a science of quantitatively studying regularity of random phenomena, which is extensively applied in natural science, technological science, social science and managerial science etc. Hence, it has been developing rapidly since 1930's and many new branches have emerged from time to time. Limit Theory is one of the branches and also an important theoretical basis of science of Probability and Statistics. As stated in the classical book "Limit distributions for sums of independent random variables"(1949) by B.V.Gendenko and A.N.Kolmogrov, "The epistemological value of the theory of probability is revealed only by limit theorems. Without limit theorems it is impossible to understand the real content of the primary concept of all our sciences-the concept of probability." Classical limit theory includes the central limit theory, the law of large numbers, and the law of iterated logarithm etc. We also call they as convergence in distribution, convergence in probability and almose sure convergence.Fridy (1985, 1993) introduced the concept of the statistical convergence by using the natural density. The first chapter introduces the concepts of statistical a.s. convergence, statistical convergence in probability, and statistical convergence in distribution respect to a.s. convergence, convergence in probability, and convergence in distribution. And some sufficient and/or necessary conditions are also given. In Chapter 2, we define the st-lim-sup and st-lim-inf on a finite set of real numbers instead of a real sequence. We use this definition to give a new method to deal with random sampling data.