Random Samples

This chapter discusses the properties of the distributions of statistics (called sampling distributions). The distributions that are introduced are of special importance in statistical inference. Today complex statistical problems are often investigated based on generated random samples from specific distributions that are easy to obtain even using available statistical software packages. The chapter introduces related concepts and explains the theory behind the Monte Carlo simulation process. It describes the definition that captures the type of convergence encountered in the law of large numbers. The strong laws of large numbers are theorems that assert almost sure convergence of sequences of random variables obtained by averaging some underlying sequences of random variables. The central limit theorem asserts that the total effect of such “small” factors is random and has approximately a normal distribution.