ABSTRACT
This chapter provides the theoretical background for fitting a distribution to a random sample of observations. It explains maximum likelihood estimators (MLEs) of the parameters. The chapter also explains properties of MLEs under a correctly specified model and how to obtain standard errors, confidence intervals, and tests. Confidence intervals based on standard errors rely on the quadratic approximation of the log-likelihood. The shape of the log-likelihood for a finite sample size mainly depends on how the probability (density) function is parameterized. A narrow confidence interval indicates an estimate with high precision, and conversely a wide confidence interval indicates an estimate with low precision.
