ABSTRACT
This chapter provides the theoretical background for fitting a distribution to data. It explains basic concepts of statistical inference. The chapter discusses also the classical frequentist and Bayesian approaches to inference. The model involves a set of assumptions on how the population is behaving and how the sample is generated from the population. A nonparametric model requires less restrictive assumptions. The Bayesian and classical frequentist schools of statistics use the likelihood function differently. Bayesian inference uses the likelihood as the only source of information about the parameters coming from the data, which is then combined with a prior distribution for the parameters to give the posterior distribution of the parameters.
